Algebras with operators, Koszul duality, and conformal algebras
|
|
|
- Basil Haynes
- 6 years ago
- Views:
Transcription
1 Algebras with operators, Koszul duality, and conformal algebras Pavel Kolesnikov Sobolev Institute of Mathematics Novosibirsk, Russia Third Mile High Conference on Nonassociative Mathematics Denver, Aug. 12, 2013
2 1 Algebras Associative, alternative, Lie, Jordan, Malcev, Poisson, Lie&Jordan triple systems, Sabinin algebras, differential algebras, Hom-algebras,... Replicaton pre-, post-algebras (Dendriform algebras) Algebras with Rota-Baxter operators Koszul duality di-, tri-algebras (Loday-type algebras) Algebras with averaging operators
3 1 Algebras Associative, alternative, Lie, Jordan, Malcev, Poisson, Lie&Jordan triple systems, Sabinin algebras, differential algebras, Hom-algebras,... Replication pre-, post-algebras (Dendriform algebras) Algebras with Rota-Baxter operators Koszul duality di-, tri-algebras (Loday-type algebras) Algebras with averaging operators
4 Example: 2 Lie Algebras Replication Left-symmetric algebras (pre-lie algebras) Leibniz Algebras [E. Vinberg, 1960] [J.-L. Koszul, 1961] [M. Gerstenhaber, 1963] [A. Bloh, 1965] [J.-L. Loday, 1993] [A. Cayley, 1896]
5 3 Pre-Lie Algebras Leibniz Algebras Combinatorics of rooted trees Deformation theory of algebras... and many others [D.Burde, 2005] Differential Geometry Conformal and vertex algebras Cohomology of Lie algebras
6 3 Pre-Lie Algebras Leibniz Algebras Combinatorics of rooted trees Deformation theory of algebras... and many others [D.Burde, 2005] Differential Geometry Conformal and vertex algebras Solutions of CYBE Cohomology of Lie algebras
7 4
8 5
9 6
10 [A. Belavin, V. Dinfeld, 1982] 7 [M. Semenov-Tian-Shansky, 1983]
11 [A. Belavin, V. Dinfeld, 1982] 7 [M. Semenov-Tian-Shansky, 1983]
12 Replicating an operad 8 Example:
13 Replicating an operad 9 [F. Chapoton, 2001]: [B. Vallette, 2008]: (Manin white product of operads [V. Ginzburg, M. Kapranov, 1994]) (Hadamard product of operads) for binary quadratic operads Definition: [P.K., 2008] [A. Pozhidaev, 2009] } binary case (di-) [M. Bremner, R. Felipe, J. Sanchez-Ortega, 2011] - general case (di-) [V. Gubarev, P.K., 2011] - binary case (tri-) [J.Pei, C. Bai, L. Guo, X. Ni, 2012] - name of the procedure
14 Replicating an operad (general tri-algebra case) 10 Bremner & Sanchez-Ortega + Gubarev & K. (Perm instead of ComTrias)
15 Replicating an operad Example: replicating a ternary operation 11
16 Replicating an operad Example: replicating a ternary operation 11 Replicating a monomial: e.g.,
17 Replicating an operad Example: replicating a ternary operation 11 Replicating a monomial: e.g.,
18 Replicating an operad Example: replicating a ternary operation 11 Replicating a monomial: e.g., any of
19 Replicating an operad Examples 12 di-lie = Leib di-com = Perm [F. Chapoton, 2001] di-as = Dias [J.-L. Loday, T. Pirashvili, 1993] di-alt [L. Dong, 2005] di-jord [M. Bremner, L. Peresi, 2011] di-jts [M. Bremner, R. Felipe, J. Sanchez-Ortega, 2011] di-mal [ M. Bremner, L. Peresi, J. Sanchez-Ortega, 2011] tri-com = ComTrias [B. Vallette, 2007] tri-as = Trias [J.-L. Loday, M. Ronco, 2004]
20 Replicating an operad 13 (c.f. [P.K., 2008], [A. Pozhidaev, 2009], [P.K., V. Voronin, 2013])
21 Replicating an operad (Averaging operators) Demo case: one binary operation 14
22 Replicating an operad (Averaging operators) Demo case: one binary operation 14
23 Replicating an operad (PBW-type problems) 15???
24 Replicating an operad (PBW-type problems) 16
25 Replicating an operad (PBW-type problems) 16
26 Replicating an operad (PBW-type problems) 16
27 Replicating an operad (PBW-type problems) 17
28 Replicating an operad (PBW-type problems) 17
29 Replicating an operad (Special identities) 18
30 Replicating an operad (Special identities) 18
31 Replicating an operad (Special identities) 19
32 Splitting an operad 20 name of the procedure The structures obtained are ``dual to di- and tri-algebras
33 Splitting an operad Koszul duality for operads [V. Ginzburg, M. Kapranov, 1994] 21 Example:
34 Splitting an operad for binary quadratic operads 22 } Black and white Manin products of binary quadratic operads
35 Splitting an operad for binary quadratic operads 23
36 Splitting an operad (Pre-algebras, general case) 24
37 Splitting an operad Example: splitting of 25
38 Splitting an operad Example: splitting of 25
39 Splitting an operad (Post-algebras, general case) 26
40 Splitting an operad 27
41 Splitting an operad 28
42 Splitting an operad (Rota-Baxter operators) Demo case: one binary operation 29 [G. Baxter, 1960] [G.-C. Rota, 1969]
43 Splitting an operad (Rota-Baxter operators) Demo case: one binary operation 30
44 Splitting an operad (Rota-Baxter operators) arbitrary operad 31
45 Splitting an operad (Rota-Baxter operators) arbitrary operad 31
46 Splitting an operad (PBW-type problems and special identities) 32
47 Splitting an operad (PBW-type problems and special identities) 32?
48 Splitting an operad (PBW-type problems and special identities) 33
49 Splitting an operad (Example) 34
50 Splitting an operad (PBW-type problems and special identities) 35 [M. Bremner, S. Madariaga, 2013]: pre-jord pre-as No special identities of degree <8 6 special identities of degree 8
51 Splitting an operad (A counterexample) 36
52 Thank you!
arxiv: v1 [math.qa] 30 Dec 2018
![arxiv: v1 [math.qa] 30 Dec 2018](/thumbs/93/111899504.jpg "arxiv: v1 [math.qa] 30 Dec 2018")
DERIVED IDENTITIES OF DIFFERENTIAL ALGEBRAS P. S. KOLESNIKOV arxiv:1812.11516v1 [math.qa] 30 Dec 2018 Abstract. Suppose A is a not necessarily associative algebra with a derivation d. Then A may be considered
arxiv: v2 [math.ra] 23 Oct 2015
![arxiv: v2 [math.ra] 23 Oct 2015](/thumbs/72/67714632.jpg "arxiv: v2 [math.ra] 23 Oct 2015")
SPLITTING OF OPERATIONS FOR ALTERNATIVE AND MALCEV STRUCTURES arxiv:1312.5710v2 [math.ra] 23 Oct 2015 SARA MADARIAGA Abstract. In this paper we define pre-malcev algebras and alternative quadrialgebras
arxiv: v1 [math.ra] 19 Dec 2013
![arxiv: v1 [math.ra] 19 Dec 2013](/thumbs/72/67170094.jpg "arxiv: v1 [math.ra] 19 Dec 2013")
SPLITTING OF OPERATIONS FOR ALTERNATIVE AND MALCEV STRUCTURES arxiv:1312.5710v1 [math.ra] 19 Dec 2013 SARA MADARIAGA Abstract. In this paper we define pre-malcev algebras and alternative quadrialgebras
SPECIAL IDENTITIES FOR THE PRE-JORDAN PRODUCT IN THE FREE DENDRIFORM ALGEBRA
SPECIAL IDENTITIES FOR THE PRE-JORDAN PRODUCT IN THE FREE DENDRIFORM ALGEBRA MURRAY R. BREMNER AND SARA MADARIAGA In memory of Jean-Louis Loday (1946 2012) Abstract. Pre-Jordan algebras were introduced
Universal Enveloping Commutative Rota Baxter Algebras of Pre- and Post-Commutative Algebras
axioms Article Universal Enveloping Commutative Rota Baxter Algebras of Pre- and Post-Commutative Algebras Vsevolod Gubarev 1,2 ID 1 Laboratory of Rings Theory, Sobolev Institute of Mathematics of the
Operads and triangulation of Loday s diagram on Leibniz algebras
Afr. Mat. (2017) 28:109 118 DOI 10.1007/s13370-016-0431-2 Operads and triangulation of Loday s diagram on Leibniz algebras Allahtan Victor Gnedbaye 1 Received: 27 September 2014 / Accepted: 22 April 2016
A brief introduction to pre-lie algebras
Chern Institute of Mathematics, Nankai University Vasteras, November 16, 2016 Outline What is a pre-lie algebra? Examples of pre-lie algebras Pre-Lie algebras and classical Yang-Baxter equation Pre-Lie
Derived bracket construction up to homotopy and Schröder numbers
arxiv:1202.0095v9 [math.qa] 29 Dec 2012 Derived bracket construction up to homotopy and Schröder numbers K. UCHINO Abstract On introduit la notion de la construction crochet dérivé supérieure dans la catégorie
Loday-type Algebras and the Rota-Baxter Relation
Loday-type Algebras and the Rota-Baxter Relation arxiv:math-ph/0207043v2 26 Aug 2002 K. Ebrahimi-Fard 1 Physikalisches Institut der Universität Bonn Nußallee 12, D 53115 Bonn, Germany Abstract In this
ALGEBRAS, DIALGEBRAS, AND POLYNOMIAL IDENTITIES. Murray R. Bremner
Serdica Math. J. 38 (2012), 91 136 ALGEBRAS, DIALGEBRAS, AND POLYNOMIAL IDENTITIES Murray R. Bremner Communicated by V. Drensky Dedicated to Yuri Bahturin on his 65th birthday Abstract. This is a survey
Classical Yang-Baxter Equation and Its Extensions
(Joint work with Li Guo, Xiang Ni) Chern Institute of Mathematics, Nankai University Beijing, October 29, 2010 Outline 1 What is classical Yang-Baxter equation (CYBE)? 2 Extensions of CYBE: Lie algebras
Research Article Rota-Baxter Operators on 3-Dimensional Lie Algebras and the Classical R-Matrices
Hindawi Advances in Mathematical Physics Volume 07, Article ID 680, 7 pages https://doi.org/0.55/07/680 Research Article Rota-Baxter Operators on 3-Dimensional Lie Algebras and the Classical R-Matrices
arxiv: v1 [math.ra] 12 Jun 2017
![arxiv: v1 [math.ra] 12 Jun 2017](/thumbs/94/121644810.jpg "arxiv: v1 [math.ra] 12 Jun 2017")
ON TORTKARA TRIPLE SYSTEMS arxiv:1706.03748v1 [math.ra] 12 Jun 2017 MURRAY BREMNER Abstract. The commutator [a,b] = ab ba in a free Zinbiel algebra (dual Leibniz algebra) is an anticommutative operation
Deformation theory of algebraic structures
Deformation theory of algebraic structures Second Congrès Canada-France June 2008 (Bruno Vallette) Deformation theory of algebraic structures June 2008 1 / 22 Data: An algebraic structure P A vector space
arxiv: v1 [math.ct] 2 Feb 2013
![arxiv: v1 [math.ct] 2 Feb 2013](/thumbs/88/117712209.jpg "arxiv: v1 [math.ct] 2 Feb 2013")
THE CATEGORY AND OPERAD OF MATCHING DIALGEBRAS YONG ZHANG, CHENGMING BAI, AND LI GUO arxiv:1302.0399v1 [math.ct] 2 Feb 2013 Abstract. This paper gives a systematic study of matching dialgebras corresponding
HOMOLOGY OF GENERALIZED PARTITION POSETS
HOMOLOGY OF GENERALIZED PARTITION POSETS BRUNO VALLETTE Abstract. We define a family of posets of partitions associated to an operad. We prove that the operad is Koszul if and only if the posets are Cohen-
Lectures on Quantum Groups
Lectures in Mathematical Physics Lectures on Quantum Groups Pavel Etingof and Olivier Schiffinann Second Edition International Press * s. c *''.. \ir.ik,!.'..... Contents Introduction ix 1 Poisson algebras
INVERSION OF INTEGRAL SERIES ENUMERATING PLANAR TREES
Séminaire Lotharingien de Combinatoire 53 (2005), Article B53d INVERSION OF INTEGRAL SERIES ENUMERATING PLANAR TREES JEAN-LOUIS LODAY Abstract. We consider an integral series f(x, t) which depends on the
PREPOISSON ALGEBRAS MARCELO AGUIAR
PREPOISSON ALGEBRAS MARCELO AGUIAR Abstract. A definition of prepoisson algebras is proposed, combining structures of prelie and zinbiel algebra on the same vector space. It is shown that a prepoisson
arxiv: v1 [math.ra] 6 Oct 2017
![arxiv: v1 [math.ra] 6 Oct 2017](/thumbs/73/68275620.jpg "arxiv: v1 [math.ra] 6 Oct 2017")
Rota Baxter operators of zero weight on simple Jordan algebra of Clifford type V. Gubarev arxiv:1710.02377v1 [math.ra] 6 Oct 2017 Abstract It is proved that any Rota Baxter operator of zero weight on Jordan
Algebras, Operads, Combinads
Algebras, Operads, Combinads Jean-Louis Loday IRMA (Cnrs) et Institut de Mathématique Zinbiel, Strasbourg HOGT Lille, 23 mars 2012 Plan of the talk I. Types of algebras, types of operads Plan of the talk
Homotopy Batalin-Vilkovisky algebras
Homotopy Batalin-Vilkovisky algebras Bruno VALLETTE (Université de Nice Sophia-Antipolis/MPIM) Seminar on Algebra, Geometry and Physics (MPIM, 14/09/09) Joint work with Imma Gálvez and Andy Tonks Overview
Deligne s. Kathryn Hess. Institute of Geometry, Algebra and Topology Ecole Polytechnique Fédérale de Lausanne
Institute of Geometry, Algebra and Topology Ecole Polytechnique Fédérale de Lausanne Colloquium Wayne State University 25 October 2010 Outline 1 cohomology 2 3 Definition [, 1945] Let k be any commutative
Remarks on deformation quantization of vertex Poisson algebras
Remarks on deformation quantization of vertex Poisson algebras Shintarou Yanagida (Nagoya) Algebraic Lie Theory and Representation Theory 2016 June 13, 2016 1 Introduction Vertex Poisson algebra (VPA)
Some Hopf Algebras of Trees. Pepijn van der Laan. Mathematisch Instituut, Universiteit Utrecht. May 22, 2001
Some Hopf Algebras of Trees Pepijn van der Laan vdlaan@math.uu.nl Mathematisch Instituut, Universiteit Utrecht May 22, 2001 1 Introduction In the literature several Hopf algebras that can be described
arxiv:math/ v2 [math.qa] 30 Mar 2005
![arxiv:math/ v2 [math.qa] 30 Mar 2005](/thumbs/92/108046435.jpg "arxiv:math/ v2 [math.qa] 30 Mar 2005")
THE OPERAD QUAD IS KOSZUL JON EIVIND VATNE arxiv:math/04580v2 [math.qa] 30 Mar 2005 Abstract. The purpose of this paper is to prove the koszulity of the operad Quad, governing quadri-algebras. That Quad
arxiv: v1 [math.ra] 11 Aug 2010
![arxiv: v1 [math.ra] 11 Aug 2010](/thumbs/91/106787441.jpg "arxiv: v1 [math.ra] 11 Aug 2010")
ON THE DEFINITION OF QUASI-JORDAN ALGEBRA arxiv:1008.2009v1 [math.ra] 11 Aug 2010 MURRAY R. BREMNER Abstract. Velásquez and Felipe recently introduced quasi-jordan algebras based on the product a b = 1
arxiv:math/ v3 [math.ra] 31 May 2007
![arxiv:math/ v3 [math.ra] 31 May 2007](/thumbs/91/105208499.jpg "arxiv:math/ v3 [math.ra] 31 May 2007")
ROTA-BAXTER ALGEBRAS AND DENDRIFORM ALGEBRAS KURUSCH EBRAHIMI-FARD AND LI GUO arxiv:math/0503647v3 [math.ra] 31 May 2007 Abstract. In this paper we study the adjoint functors between the category of Rota-
A short survey on pre-lie algebras
A short survey on pre-lie algebras Dominique Manchon Abstract. We give an account of fundamental properties of pre-lie algebras, and provide several examples borrowed from various domains of Mathematics
Rota-Baxter Algebra I
1 Rota-Baxter Algebra I Li GUO Rutgers University at Newark . From differentiation to integration. d Differential operator: dx (f)(x) = lim h differential equations differential geometry differential topology
Deformations of ternary algebras
Journal of Generalized Lie Theory and Applications Vol. 1 (2007), No. 1, 41 55 Deformations of ternary algebras Hammimi ATAGUEMA and Abdenacer MAKHLOUF University of Haute Alsace, Laboratoire de Mathématiques,
Higher Algebra with Operads
University of Nice Sophia Antipolis (Newton Institute, Cambridge) British Mathematical Colloquium March 27, 2013 Plan 1 2 3 Multicomplexes A -algebras Homotopy data and mixed complex structure Homotopy
Unital associahedra. and homotopy unital homotopy associative algebras. Andrew TONKS London Metropolitan University
Unital associahedra and homotopy unital homotopy associative algebras Andrew TONKS London Metropolitan University with Fernando MURO Universidad de Sevilla Outline Classical algebraic definition arises
An Introduction to Rota-Baxter Algebra
Surveys of Modern Mathematics Volume IV An Introduction to Rota-Baxter Algebra Li Guo International Press www.intlpress.com HIGHER EDUCATION PRESS Surveys of Modern Mathematics, Volume IV An Introduction
Semilattices of r-archimedean subdimonoids
BULETINUL ACADEMIEI DE ŞTIINŢE A REPUBLICII MOLDOVA. MATEMATICA Number 3(67), 2011, Pages 108 112 ISSN 1024 7696 Semilattices of r-archimedean subdimonoids Anatolii V. Zhuchok Abstract. We characterize
Koszul duality for operads
Koszul duality for operads Bruno Vallette (This is in Chapters 6 and 7 of Loday-Vallette; we ll do exercises 1,7,8,9,10.) 1 Motivation We are interested in an arbitrary of P -algebras. We would like to
From Rota-Baxter Algebras to Pre-Lie Algebras
From Rota-Baxter lgebras to Pre-Lie lgebras Huihui n a Chengming Bai b a. Department of Mathematics & LPMC, Nankai University, Tianjin 37, P.R. China arxiv:7.39v [math-ph] 9 Nov 27 b. Chern Institute of
On the Lie envelopping algebra of a pre-lie algebra
On the Lie envelopping algebra of a pre-lie algebra Jean-Michel Oudom, Daniel Guin To cite this version: Jean-Michel Oudom, Daniel Guin. On the Lie envelopping algebra of a pre-lie algebra. Journal of
Enveloping algebras of Hom-Lie algebras
Journal of Generalized Lie Theory and Applications Vol. 2 (2008), No. 2, 95 108 Enveloping algebras of Hom-Lie algebras Donald YAU Department of Mathematics, The Ohio State University at Newark, 1179 University
Constructing Hom-Poisson Color Algebras
International Journal of Algebra, Vol. 13, 2019, no. 1, 1-16 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ija.2019.81137 Constructing Hom-Poisson Color Algebras Ibrahima Bakayoko University of
arxiv:math/ v1 [math.qa] 9 Nov 2003
![arxiv:math/ v1 [math.qa] 9 Nov 2003](/thumbs/92/109196059.jpg "arxiv:math/ v1 [math.qa] 9 Nov 2003")
Construction of Nijenhuis operators and dendriform trialgebras 1 Philippe Leroux Institut de Recherche Mathématique, Université de Rennes I and CNRS UMR 6625 Campus de Beaulieu, 35042 Rennes Cedex, France,
DEFORMATION OF LEIBNIZ ALGEBRA MORPHISMS
Homology, Homotopy and Applications, vol. 9(1), 2007, pp.439 450 DEFORMATION OF LEIBNIZ ALGEBRA MORPHISMS ASHIS MANDAL (communicated by Jean-Louis Loday) Abstract We study formal deformations of Leibniz
Some constructions and applications of Rota-Baxter algebras I
Some constructions and applications of Rota-Baxter algebras I Li Guo Rutgers University at Newark joint work with Kurusch Ebrahimi-Fard and William Keigher 1. Basics of Rota-Baxter algebras Definition
Rota-Baxter operators on pre-lie algebras
Journal of Nonlinear Mathematical Physics Volume 14, Number (007), 69 89 Article Rota-Baxter operators on pre-lie algebras Xiuxian LI a,b, Dongping HOU a and Chengming BAI c a Department of Mathematics
Hypercommutative Operad as a Homotopy QuotientofBV
Commun. Math. Phys. 322, 697 729 2013 Digital Object Identifier DOI 10.1007/s00220-013-1737-7 Communications in Mathematical Physics Hypercommutative Operad as a Homotopy QuotientofBV A. Khoroshkin 1,2,
Nonassociative Lie Theory
Ivan P. Shestakov The International Conference on Group Theory in Honor of the 70th Birthday of Professor Victor D. Mazurov Novosibirsk, July 16-20, 2013 Sobolev Institute of Mathematics Siberian Branch
Embedding dendriform dialgebra into its universal enveloping Rota-Baxter algebra
Embedding dendriform dialgebra into its universal enveloping Rota-Baxter algebra arxiv:1005.2717v1 [math.ra] 16 May 2010 Yuqun Chen and Qiuhui Mo School of Mathematical Sciences, South China Normal University
Rational Homotopy and Intrinsic Formality of E n -operads Part II
Rational Homotopy and Intrinsic Formality of E n -operads Part II Benoit Fresse Université de Lille 1 φ 1 2 3 1 2 Les Diablerets, 8/23/2015 3 ( exp 1 2 3 ˆL }{{} t 12, 1 2 3 ) }{{} t 23 Benoit Fresse (Université
Operads Hopf algebras and coloured Koszul duality
Operads Hopf algebras and coloured Koszul duality PH.D. THESIS OF PEPIJN VAN DER LAAN AT UTRECHT UNIVERSITY JANUARY 12TH, 2004 TER NAGEDACHTENIS AAN Dr. Anthonie van Heemert (Wiskundige, 1912 1968) Ignoro
arxiv:math/ v1 [math.dg] 5 Jan 2004
![arxiv:math/ v1 [math.dg] 5 Jan 2004](/thumbs/78/77803677.jpg "arxiv:math/ v1 [math.dg] 5 Jan 2004")
PROP profile of Poisson geometry S.A. Merkulov arxiv:math/040034v [math.dg] 5 Jan 004 The genetic code appears to be universal;... Britannica. 0. Abstract. The first instances of algebraic and topological
Abstracts of Talks. Third Mile High Conference on Nonassociative Mathematics August 11 17,2013 University of Denver, Denver, Colorado
Abstracts of Talks Third Mile High Conference on Nonassociative Mathematics August 11 17,2013 University of Denver, Denver, Colorado (updated August 9, 2013) Representation groups of finite Osborn loops
Centroids Of Dendriform Algebras
Volume 9 No. 5 208, 427-435 ISSN 34-3395 (on-line version) url http//www.acadpubl.eu/hub/ http//www.acadpubl.eu/hub/ Centroids Of Dendriform Algebras Mohammed Abdul Daim Zoba College of Engineering\ Al-Musayab,
Anatolii V. Zhuchok SOME SEMILATTICE DECOMPOSITIONS OF DIMONOIDS
DEMONSTRATIO MATHEMATICA Vol. XLIV No 3 2011 Anatolii V. Zhuchok SOME SEMILATTICE DECOMPOSITIONS OF DIMONOIDS Abstract. We show that the system of axioms of a dimonoid is independent and prove that every
arxiv: v1 [math.ra] 11 Aug 2016
![arxiv: v1 [math.ra] 11 Aug 2016](/thumbs/76/73253980.jpg "arxiv: v1 [math.ra] 11 Aug 2016")
Ternary Leibniz color algebras and beyond arxiv:1608.03505v1 [math.ra] 11 Aug 2016 Ibrahima BAKAYOKO Département de Mathématiques, Centre Universitaire de N Zérékoré/UJNK BP 50 N Zérékoré, Guinée. Abstract.
arxiv: v1 [math.ra] 11 Apr 2016
![arxiv: v1 [math.ra] 11 Apr 2016](/thumbs/72/66974637.jpg "arxiv: v1 [math.ra] 11 Apr 2016")
arxiv:1604.02950v1 [math.ra] 11 Apr 2016 Rota-Baxter coalgebras and Rota-Baxter bialgebras Tianshui Ma and Linlin Liu 1 Department of Mathematics, School of Mathematics and Information Science, Henan Normal
Gröbner-Shirshov Bases and PBW Theorems
Journal of Siberian Federal University. Mathematics & Physics 2013, 6(4), 417 427 УДК 512.5 Leonid A. Bokut Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia School of Mathematical Sciences,
arxiv: v4 [math.kt] 11 May 2011
![arxiv: v4 [math.kt] 11 May 2011](/thumbs/92/108483227.jpg "arxiv: v4 [math.kt] 11 May 2011")
FREE RESOLUTIONS VIA GRÖBNER BASES arxiv:0912.4895v4 [math.kt] 11 May 2011 VLADIMIR DOTSENKO AND ANTON KHOROSHKIN Abstract. For associative algebras in many different categories, it is possible to develop
Houston Journal of Mathematics. c 2016 University of Houston Volume 42, No. 1, 2016
Houston Journal of Mathematics c 2016 University of Houston Volume 42, No. 1, 2016 DIRECTIONAL ALGEBRAS J.D.H. SMITH Communicated by Mai Gehrke Abstract. Directional algebras are generalizations of dimonoids,
LIE CENTRAL TRIPLE RACKS. Guy Roger Biyogmam
International Electronic Journal of Algebra Volume 17 (2015) 58-65 LIE CENTRAL TRIPLE RACKS Guy Roger Biyogmam Received: 18 February 2014; Revised 2 September 2014 Communicated by A. Çiğdem Özcan Abstract.
Plan Feynman categories Universal constructions. Feynman categories. Ralph Kaufmann. IAS and Purdue University. IAS, Dec
Feynman categories Ralph Kaufmann IAS and Purdue University IAS, Dec 6. 2013 References Main paper(s) with B. Ward and J. Zuniga. 1 Feynman categories: Arxiv 1312.1269 2 Examples in: The odd origin of
FREE MONOID IN MONOIDAL ABELIAN CATEGORIES
Abstract. We give an explicit construction of the free monoid in monoidal abelian categories when the monoidal product does not necessarily preserve coproducts. Then we apply it to several new monoidal
Factorization of the Loop Algebras and Compatible Lie Brackets
Journal of Nonlinear Mathematical Physics Volume 12, Supplement 1 (2005), 343 350 Birthday Issue Factorization of the Loop Algebras and Compatible Lie Brackets I Z GOLUBCHIK and V V SOKOLOV Ufa Pedagogical
DEFORMATIONS OF BATALIN VILKOVISKY ALGEBRAS
POISSON GEOMETRY BANACH CENTER PUBLICATIONS, VOLUME 51 INSTITUTE OF MATHEMATICS POLISH ACADEMY OF SCIENCES WARSZAWA 2000 DEFORMATIONS OF BATALIN VILKOVISKY ALGEBRAS OLGA KRAVCHENKO Institut Girard Desargues
FOURIER - SATO TRANSFORM BRAID GROUP ACTIONS, AND FACTORIZABLE SHEAVES. Vadim Schechtman. Talk at
, BRAID GROUP ACTIONS, AND FACTORIZABLE SHEAVES Vadim Schechtman Talk at Kavli Institute for the Physics and Mathematics of the Universe, Kashiwa-no-ha, October 2014 This is a report on a joint work with
Derived brackets and sh Leibniz algebras
Derived brackets and sh Leibniz algebras arxiv:0902.0044v7 [math.qa] 23 Jun 2010 K. UCHINO Abstract We will give a generalized framework for derived bracket construction. It will be shown that a deformation
PBW for an inclusion of Lie algebras
PBW for an inclusion of Lie algebras Damien Calaque, Andrei Căldăraru, Junwu Tu Abstract Let h g be an inclusion of Lie algebras with quotient h-module n. There is a natural degree filtration on the h-module
OPERADS OF FINITE POSETS
OPERADS OF FINITE POSETS Abstract. We describe four natural operad structures on the vector space generated by isomorphism classes of finite posets. The three last ones are set-theoretical and can be seen
Poisson and Hochschild cohomology and the semiclassical limit
Poisson and Hochschild cohomology and the semiclassical limit Matthew Towers University of Kent http://arxiv.org/abs/1304.6003 Matthew Towers (University of Kent) arxiv 1304.6003 1 / 15 Motivation A quantum
CONSTRUCTION OF NIJENHUIS OPERATORS AND DENDRIFORM TRIALGEBRAS
IJMMS 2004:49, 2595 2615 PII. S0161171204402117 http://ijmms.hindawi.com Hindawi Publishing Corp. CONSTRUCTION OF NIJENHUIS OPERATORS AND DENDRIFORM TRIALGEBRAS PHILIPPE LEROUX Received 16 February 2004
A spectral sequence for the homology of a finite algebraic delooping
A spectral sequence for the homology of a finite algebraic delooping Birgit Richter joint work in progress with Stephanie Ziegenhagen Lille, October 2012 Aim: 1) Approximate Quillen homology for E n -algebras
A.S. DZHUMADIL DAEV, N.A. ISMAILOV, AND F. A. MASHUROV
EMBEDDABLE ALGEBRAS INTO ZINBIEL ALGEBRAS VIA THE COMMUTATOR arxiv:1809.10550v1 [math.ra] 27 Sep 2018 A.S. DZHUMADIL DAEV, N.A. ISMAILOV, AND F. A. MASHUROV Abstract. A criterion for elements of free Zinbiel
CURRICULUM VITAE. Name: Yuqun Chen Sex: Male Place of Birth: P.R. China
CURRICULUM VITAE Name: Yuqun Chen Sex: Male Place of Birth: P.R. China Address: School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China Email: yqchen@scnu.edu.cn Telephone:
DEFORMATIONS OF ALGEBRAS IN NONCOMMUTATIVE ALGEBRAIC GEOMETRY EXERCISE SHEET 1
DEFORMATIONS OF ALGEBRAS IN NONCOMMUTATIVE ALGEBRAIC GEOMETRY EXERCISE SHEET 1 TRAVIS SCHEDLER Note: it is possible that the numbers referring to the notes here (e.g., Exercise 1.9, etc.,) could change
CLASSICAL R-MATRICES AND NOVIKOV ALGEBRAS
CLASSICAL R-MATRICES AND NOVIKOV ALGEBRAS DIETRICH BURDE Abstract. We study the existence problem for Novikov algebra structures on finite-dimensional Lie algebras. We show that a Lie algebra admitting
arxiv: v2 [math.ra] 25 Nov 2012
![arxiv: v2 [math.ra] 25 Nov 2012](/thumbs/93/117980495.jpg "arxiv: v2 [math.ra] 25 Nov 2012")
PRE-LIE ALGEBRAS IN POSITIVE CHARACTERISTIC arxiv:1011.4217v2 [math.ra] 25 Nov 2012 IOANNIS DOKAS Abstract. In rime characteristic we introduce the notion of restricted re- Lie algebras. We rove in the
arxiv: v1 [math.ra] 22 Jan 2018
![arxiv: v1 [math.ra] 22 Jan 2018](/thumbs/88/116083445.jpg "arxiv: v1 [math.ra] 22 Jan 2018")
Rota Baxter Operators on Quadratic Algebras Pilar Benito, Vsevolod Gubarev and Alexander Pozhidaev arxiv:1801.07037v1 [math.ra] 22 Jan 2018 Abstract. We prove that all Rota Baxter operators on a quadratic
arxiv:math/ v2 [math.ra] 30 Nov 2005 On Hopf algebra structures over operads
![arxiv:math/ v2 [math.ra] 30 Nov 2005 On Hopf algebra structures over operads](/thumbs/94/121074254.jpg "arxiv:math/ v2 [math.ra] 30 Nov 2005 On Hopf algebra structures over operads")
arxiv:math/0407074v2 [math.ra] 30 Nov 2005 On Hopf algebra structures over operads Ralf Holtkamp Fakultät für Mathematik Ruhr-Universität Bochum 2004 2 11/2005 Contents Introduction 5 1 Basic Concepts.
A Leibniz Algebra Structure on the Second Tensor Power
Journal of Lie Theory Volume 12 (2002) 583 596 c 2002 Heldermann Verlag A Leibniz Algebra Structure on the Second Tensor Power R. Kurdiani and T. Pirashvili Communicated by K.-H. Neeb Abstract. For any
FROM THE FORMALITY THEOREM OF KONTSEVICH AND CONNES-KREIMER ALGEBRAIC RENORMALIZATION TO A THEORY OF PATH INTEGRALS
FROM THE FORMALITY THEOREM OF KONTSEVICH AND CONNES-KREIMER ALGEBRAIC RENORMALIZATION TO A THEORY OF PATH INTEGRALS Abstract. Quantum physics models evolved from gauge theory on manifolds to quasi-discrete
arxiv:math/ v3 [math.ra] 15 Jul 2007
![arxiv:math/ v3 [math.ra] 15 Jul 2007](/thumbs/72/66750147.jpg "arxiv:math/ v3 [math.ra] 15 Jul 2007")
QUADRATIC ALGEBRAS RELATED TO THE BI-HAMILTONIAN OPERAD MIKHAIL BERSHTEIN, VLADIMIR DOTSENKO, AND ANTON KHOROSHKIN arxiv:math/060789v3 [math.ra] 15 Jul 007 Abstract. We prove the conjectures on dimensions
On the operad of associative algebras with derivation
Georgian Math. J. (2010), 26 pages DOI 10.1515/GMJ.2010.010 de Gruyter 2010 On the operad of associative algebras with derivation Jean-Louis Loday Abstract. We study the operad of associative algebras
Unexpected facets of the Yang-Baxter equation
Unexpected facets of the Yang-Baxter equation Victoria LEBED University of Nantes Utrecht, September 29, 2015 1 Yang-Baxter equation Avectorspace V(oranobjectinany monoidal category) σ: V 2 V 2 Yang-Baxter
PROPped up graph cohomology
PROPped up graph cohomology M. Markl and A.A. Voronov 2 Instutute of Mathematics, Academy of Sciences, Žitná 25, 5 67 Praha, The Czech Republic, markl@math.cas.cz 2 School of Mathematics, University of
Dyson Schwinger equations in the theory of computation
Dyson Schwinger equations in the theory of computation Ma148: Geometry of Information Caltech, Spring 2017 based on: Colleen Delaney,, Dyson-Schwinger equations in the theory of computation, arxiv:1302.5040
ON THE (CO)HOMOLOGY OF THE POSET OF WEIGHTED PARTITIONS
ON THE (CO)HOMOLOGY OF THE POSET OF WEIGHTED PARTITIONS RAFAEL S. GONZÁLEZ D LEÓN AND MICHELLE L. WACHS Abstract. We consider the poset of weighted partitions Π w n, introduced by Dotsenko and Khoroshkin
The Toda Lattice. Chris Elliott. April 9 th, 2014
The Toda Lattice Chris Elliott April 9 th, 2014 In this talk I ll introduce classical integrable systems, and explain how they can arise from the data of solutions to the classical Yang-Baxter equation.
On the Structure of Split Leibniz Triple Systems
Acta Mathematica Sinica, English Series Oct., 2015, Vol. 31, No. 10, pp. 1629 1644 Published online: September 15, 2015 DOI: 10.1007/s10114-015-4800-9 Http://www.ActaMath.com Acta Mathematica Sinica, English
FREE DENDRIFORM ALGEBRAS. PART I. A PARENTHESIS SETTING
FREE DENDRIFORM ALGEBRAS. PART I. A PARENTHESIS SETTING PHILIPPE LEROUX Received 25 September 2005; Revised 18 September 2006; Accepted 21 September 2006 We propose both a reformulation of some known results
KOSZUL DUALITY FOR OPERADS
Vol. 76, No. 1 DUKE MATHEMATICAL JOURNAL (C) October 1994 KOSZUL DUALITY FOR OPERADS VICTOR GINZBURG AND MIKHAIL KAPRANOV 0. Introduction 1. Operads in algebra and geometry 2. Quadratic operads 3. Duality
Gröbner Shirshov bases and their calculation
Bull. Math. Sci. (2014) 4:325 395 DOI 10.1007/s13373-014-0054-6 Gröbner Shirshov bases and their calculation L. A. Bokut Yuqun Chen Received: 3 December 2013 / Revised: 3 July 2014 / Accepted: 13 August
ON A HIGHER STRUCTURE ON OPERADIC DEFORMATION COMPLEXES
Theory and Applications of Categories, Vol. 33, No. 32, 2018, pp. 988 1030. ON A HIGHER STRUCTURE ON OPERADIC DEFORMATION COMPLEXES BORIS SHOIKHET Abstract. In this paper, we prove that there is a canonical
Past Research Sarah Witherspoon
Past Research Sarah Witherspoon I work on the cohomology, structure, and representations of various types of rings, such as Hopf algebras and group-graded algebras. My research program has involved collaborations
Lie theory for quasi-shuffle bialgebras
Lie theory for quasi-shuffle bialgebras Loïc Foissy and Frédéric Patras 1 Introduction Enveloping algebras of Lie algebras are known to be a fundamental notion, for an impressive variety of reasons. Their
Erratum to: A Proof of Tsygan s Formality Conjecture for an Arbitrary Smooth Manifold
Erratum to: A Proof of Tsygan s Formality Conjecture for an Arbitrary Smooth Manifold Vasiliy A. Dolgushev Abstract Boris Shoikhet noticed that the proof of lemma 1 in section 2.3 of [1] contains an error.
arxiv:hep-th/ v1 30 Sep 1994
Distributive laws and the Koszulness Martin Markl arxiv:hep-th/9409192v1 30 Sep 1994 Introduction The basic motivation for our work was the following result of Getzler and Jones [5]. Let C n = {C n (m);
CYCLIC OPERADS AND CYCLIC HOMOLOGY
CYCLIC OPERADS AND CYCLIC HOMOLOGY E. GETZLER AND M.M. KAPRANOV The cyclic homology of associative algebras was introduced by Connes [4] and Tsygan [22] in order to extend the classical theory of the Chern
The endomorphism semigroup of a free dimonoid of rank 1
BULETINUL ACADEMIEI DE ŞTIINŢE A REPUBLICII MOLDOVA. MATEMATICA Number 3(76), 2014, Pages 30 37 ISSN 1024 7696 The endomorphism semigroup of a free dimonoid of rank 1 Yurii V.Zhuchok Abstract. We describe
Gröbner Shirshov bases and their calculation
arxiv:1303.5366v3 [math.ra] 5 Nov 2014 Gröbner Shirshov bases and their calculation L. A. Bokut Sobolev Institute of Mathematics and Novosibirsk State University, Novosibirsk 630090, Russia School of Mathematical
arxiv:math/ v1 [math.co] 6 Dec 2005
![arxiv:math/ v1 [math.co] 6 Dec 2005](/thumbs/93/113728211.jpg "arxiv:math/ v1 [math.co] 6 Dec 2005")
arxiv:math/05111v1 [math.co] Dec 005 Unimodality and convexity of f-vectors of polytopes Axel Werner December, 005 Abstract We consider unimodality and related properties of f-vectors of polytopes in various
The geometry and algebra of master equations, BV operators and Feynman transforms
The geometry and algebra of master equations, BV operators and Feynman transforms Ralph Kaufmann Purdue University and MPIM Bonn University of Pittsburgh, May 14, 2014 References Main papers with B. Ward