Compatible lie brackets and the Yang-Baxter equation

被引：26

作者：

Golubchik, IZ ^{[1
]}

Sokolov, VV

机构：

[1] Bashkir State Univ, Ufa 450074, Russia

[2] Russian Acad Sci, LD Landau Theoret Phys Inst, Moscow 117901, Russia

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 2006年 / 146卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

Yang-Baxter equation; Lie bialgebra; Manin triple;

D O I：

10.1007/s11232-006-0016-6

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We show, that any pair of compatible Lie brackets with a common invariant form produces a nonconstant solution of the classical Yang Baxter equation. We describe the corresponding Poisson brackets, Manin triples, and Lie bialgebras. It turns out that all bialgebras associated with the solutions found by Belavin and Drinfeld are isomorphic to some bialgebras generated by our solutions. For any compatible pair, we construct a double with a, common invariant form and find the corresponding solution of the quantum Yang Baxter equation for this double.

引用

页码：159 / 169

页数：11

共 50 条

[1] Compatible Lie Brackets and the Yang-Baxter Equation
I. Z. Golubchik
V. V. Sokolov
Theoretical and Mathematical Physics, 2006, 146 : 159 - 169
[2] POISSON BRACKETS ASSOCIATED WITH THE CLASSICAL YANG-BAXTER EQUATION
GUREVICH, DI
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 1989, 23 (01) : 57 - 59
[3] Dynamical Yang-Baxter equation and quantization of certain Poisson brackets
Karolinsky, E
Stolin, A
Tarasov, V
Noncommutative Geometry and Representation Theory in Mathematical Physics, 2005, 391 : 175 - 182
[4] The classical dynamical Yang-Baxter equation and Lie algebroids
Bangoura, M
Kosmann-Schwarzbach, Y
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1998, 327 (06): : 541 - 546
[5] YANG-BAXTER EQUATION AND GENERALIZATION OF THE LIE FORMAL THEORY
GUREVICH, DI
DOKLADY AKADEMII NAUK SSSR, 1986, 288 (04): : 797 - 801
[6] GRADED LIE-ALGEBRAS IN THE YANG-BAXTER EQUATION
AVAN, J
PHYSICS LETTERS B, 1990, 245 (3-4) : 491 - 496
[7] YANG-BAXTER EQUATION AND DEFORMATION OF ASSOCIATIVE AND LIE-ALGEBRAS
GUREVICH, D
RUBTSOV, V
LECTURE NOTES IN MATHEMATICS, 1992, 1510 : 47 - 55
[8] OPERATOR FORMS OF THE CLASSICAL YANG-BAXTER EQUATION IN LIE SUPERALGEBRAS
Wang, Yan
Hou, Dongping
Bai, Chengming
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2010, 7 (04) : 583 - 597
[9] THE YANG-BAXTER AND PENTAGON EQUATION
VANDAELE, A
VANKEER, S
COMPOSITIO MATHEMATICA, 1994, 91 (02) : 201 - 221
[10] INTRODUCTION TO THE YANG-BAXTER EQUATION
JIMBO, M
INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 1989, 4 (15): : 3759 - 3777

← 1 2 3 4 5 →