Parameter-dependent associative Yang-Baxter equations and Poisson brackets

被引：8

作者：

Odesskii, Alexander ^{[1
]}

Rubtsov, Vladimir ^{[2
,3
]}

Sokolov, Vladimir ^{[4
]}

机构：

[1] Brock Univ, Dept Math, St Catharines, ON L2S 3A1, Canada

[2] Univ Angers, Dept Math, LAREMA, CNRS UMR 6093, F-49045 Angers 01, France

[3] Inst Theoret & Expt Phys, Moscow 117259, Russia

[4] Landau Inst Theoret Phys, Moscow, Russia

来源：

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS | 2014年 / 11卷 / 09期

关键词：

Poisson brackets; double Poisson structures; Yang-Baxter equations; ALGEBRAS;

D O I：

10.1142/S0219887814600366

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We discuss associative analogues of classical Yang-Baxter equation (CYBE) meromorphically dependent on parameters. We discover that such equations enter in a description of a general class of parameter-dependent Poisson structures and double Lie and Poisson structures in sense of Van den Bergh. We propose a classification of all solutions for onedimensional associative Yang-Baxter equations (AYBE).

引用

页数：18

共 18 条

[1] On the associative analog of Lie bialgebras [J].

Aguiar, M .

JOURNAL OF ALGEBRA, 2001, 244 (02) :492-532

[2]

BELAVIN AA, 1982, FUNCT ANAL APPL+, V16, P159

[3]

Burban I, 2012, MEM AM MATH SOC, V220, P1

[4] Poisson structures on moduli spaces of representations [J].

Crawley-Boevey, William .

JOURNAL OF ALGEBRA, 2011, 325 (01) :205-215

[5]

Fomin S., 1999, Advances in geometry

[6]

Prog. in Mathematics book series, V172, P147

[7]

Kontsevich Maxim, 1993, GELFAND MATH SEMINAR, P173

[8] Integrable ODEs on associative algebras [J].

Mikhailov, AV ;

Sokolov, VV .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2000, 211 (01) :231-251

[9] Bi-Hamiltonian ordinary differential equations with matrix variables [J].

Odesskii, A. V. ;

Rubtsov, V. N. ;

Sokolov, V. V. .

THEORETICAL AND MATHEMATICAL PHYSICS, 2012, 171 (01) :442-447

[10] Pairs of compatible associative algebras, classical Yang-Baxter equation and quiver representations [J].

Odesskii, Alexander ;

Sokolov, Vladimir .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2008, 278 (01) :83-99

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