Some Remarks on the Classication of Poisson Lie Groups
Some Remarks on the Classication of Poisson Lie Groups
复制标题
关于泊松李群分类的一些评论
DOI：
10.1090/conm/179/01932
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发表时间：
1996
影响因子：
4.4
通讯作者：
J. Rawnsley
中科院分区：
文献类型：
--
作者：
M. Cahen;S. Gutt;J. Rawnsley
本文给出了有限维李代数上双代数结构分类问题的一些结果。我们考虑这个问题的两个方面。一个是看哪些李代数出现（直到同构）作为马宁三元组中的大代数，另一个是试图确定给定半单李代数的所有精确泊松结构。我们在这里遵循我们中的一个人在横滨研讨会上所作的演讲的介绍;特别是，我们回顾了许多众所周知的性质，因此它基本上是独立的。
We describe some results in the problem of classifying the bialgebra structures on a given nite dimensional Lie algebra. We consider two aspects of this problem. One is to see which Lie algebras arise (up to isomorphism) as the big algebra in a Manin triple, and the other is to try and determine all the exact Poisson structures for a given semisimple Lie algebra. We follow here the presentation of the talk that one of us gave at the Yokohama Symposium; in particular, we recall many well known properties so that it is essentially self-contained.