Symmetric algebras and Yang-Baxter equation

Beidar, K., Fong, Y., and Stolin, A.. "Symmetric algebras and Yang-Baxter equation." Proceedings of the 16th Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 1997. [15]-28. <http://eudml.org/doc/221831>.

@inProceedings{Beidar1997,
abstract = {Let $U$ be an open subset of the complex plane, and let $L$ denote a finite-dimensional complex simple Lie algebra. A. A. Belavin and V. G. Drinfel’d investigated non-degenerate meromorphic functions from $U\times U$ into $L\otimes L$ which are solutions of the classical Yang-Baxter equation [Funct. Anal. Appl. 16, 159-180 (1983; Zbl 0504.22016)]. They found that (up to equivalence) the solutions depend only on the difference of the two variables and that their set of poles forms a discrete (additive) subgroup $\Gamma $ of the complex numbers (of rank at most 2). If $\Gamma $ is non-trivial, they were able to completely classify all possible solutions. If $\Gamma $ is trivial, the solutions are called rational and for $L= sl_n(\mathbb \{C\})$ they were classified by A. Stolin [in Math. Scand. 69, No. 1, 57-80 (1991; Zbl 0727.17005)]. A Lie algebra $L$ is called symmetric if there exists a non-degenerate symmetric invariant bilinear form on $L$. In the !},
author = {Beidar, K., Fong, Y., Stolin, A.},
booktitle = {Proceedings of the 16th Winter School "Geometry and Physics"},
keywords = {Proceedings; Winter school; Srní (Czech Republic); Geometry; Physics},
location = {Palermo},
pages = {[15]-28},
publisher = {Circolo Matematico di Palermo},
title = {Symmetric algebras and Yang-Baxter equation},
url = {http://eudml.org/doc/221831},
year = {1997},
}

TY - CLSWK
AU - Beidar, K.
AU - Fong, Y.
AU - Stolin, A.
TI - Symmetric algebras and Yang-Baxter equation
T2 - Proceedings of the 16th Winter School "Geometry and Physics"
PY - 1997
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [15]
EP - 28
AB - Let $U$ be an open subset of the complex plane, and let $L$ denote a finite-dimensional complex simple Lie algebra. A. A. Belavin and V. G. Drinfel’d investigated non-degenerate meromorphic functions from $U\times U$ into $L\otimes L$ which are solutions of the classical Yang-Baxter equation [Funct. Anal. Appl. 16, 159-180 (1983; Zbl 0504.22016)]. They found that (up to equivalence) the solutions depend only on the difference of the two variables and that their set of poles forms a discrete (additive) subgroup $\Gamma $ of the complex numbers (of rank at most 2). If $\Gamma $ is non-trivial, they were able to completely classify all possible solutions. If $\Gamma $ is trivial, the solutions are called rational and for $L= sl_n(\mathbb {C})$ they were classified by A. Stolin [in Math. Scand. 69, No. 1, 57-80 (1991; Zbl 0727.17005)]. A Lie algebra $L$ is called symmetric if there exists a non-degenerate symmetric invariant bilinear form on $L$. In the !
KW - Proceedings; Winter school; Srní (Czech Republic); Geometry; Physics
UR - http://eudml.org/doc/221831
ER -