论文标题
在循环代数上的标准谎言lie bialgebra结构的经典曲折的分类
Classification of classical twists of the standard Lie bialgebra structure on a loop algebra
论文作者
论文摘要
仿射kac-moody代数上的标准lie bialgebra结构在下面的环代数及其抛物线亚代代代数上诱导了lie bialgebra结构。在本文中，我们将诱发的liebebra结构的所有经典曲折从Belavin-Drinfeld Quadruples角度分类为自然的等效概念。为了获得此分类，我们首先表明诱导的双齿结构是由带有两个参数的经典Yang-baxter方程（CYBE）的某些解决方案定义的。然后，使用Cybe的代数几何理论，基于无扭转的相干滑轮，我们将问题减少到Belavin和Drinfeld给出的三角溶液的众所周知分类。在抛物线副总词法的情况下，Twist的分类使我们能够回答有关CYBE所谓的准三角法解决方案的最近提出的问题。
The standard Lie bialgebra structure on an affine Kac-Moody algebra induces a Lie bialgebra structure on the underlying loop algebra and its parabolic subalgebras. In this paper we classify all classical twists of the induced Lie bialgebra structures in terms of Belavin-Drinfeld quadruples up to a natural notion of equivalence. To obtain this classification we first show that the induced bialgebra structures are defined by certain solutions of the classical Yang-Baxter equation (CYBE) with two parameters. Then, using the algebro-geometric theory of CYBE, based on torsion free coherent sheaves, we reduce the problem to the well-known classification of trigonometric solutions given by Belavin and Drinfeld. The classification of twists in the case of parabolic subalgebras allows us to answer recently posed open questions regarding the so-called quasi-trigonometric solutions of CYBE.
