LIE-POISSON GROUPS - REMARKS AND EXAMPLES

被引：5

作者：

CAHEN, M

GUTT, S

OHN, C

PARKER, M

机构：

[1] Université Libre de Bruxelles, Brussels, 1050, Campus de la Plaine, Bd. du Triomphe

来源：

LETTERS IN MATHEMATICAL PHYSICS | 1990年 / 19卷 / 04期

关键词：

AMS subject classifications (1980): 22E46; 53C57; 81C25;

D O I：

10.1007/BF00429954

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The aim of this Letter is twofold. On the one hand, we discuss two possible definitions of complex structures on Poisson-Lie groups and we give a complete classification of the isomorphism classes of complex Lie-Poisson structures on the group SL(2, ℂ). On the other hand, we give an algebraic characterization of a class of solutions of the Yang-Baxter equations which contains the well-known Drinfeld solutions [1]; in particular, we prove the existence of a nontrivial Lie-Poisson structure on any simply connected real semi-simple Lie Group G. Other low dimensional examples will appear elsewhere. © 1990 Kluwer Academic Publishers.

引用

页码：343 / 353

页数：11