例外型与Cartan型单模李超代数群阶化的分类

本项目研究某些重要单模李超代数群阶化的分类问题.主要内容分为俩个方面:.1)拟类比特征零域上例外型单李超代数所有群阶化与精细群阶化的分类,根据例外型单模李超代数D(2,1;a),G(3),F(4)的结构,利用Loop代数群阶化与仿射群概型等基本工具,确定例外型单模李超代数D(2,1;a),G(3),F(4)所有群阶化与精细群阶化的分类;.2)拟类比Cartan型单模李代数所有群阶化与精细群阶化的分类,根据Cartan型单模李超代数W,S,H,K的结构,利用Cayley代数群阶化与仿射群概型等基本工具,确定Cartan型单模李超代数W,S,H,K所有群阶化与精细群阶化的分类..单模李超代数分类尚未完成,已知单模李超代数具有重要意义,确定单模李超代数的群阶化分类是重要研究课题.

The aim of this project is to determine the classifications of group gradings for some important simple modular Lie superalgebras.The main components are divided into two parts: ..1)By analogy of the classifications of all group gradings and fine group gradings for exceptional simple Lie superalgebras over the field of characteristic 0,according to the structures of exceptional simple modular Lie superalgebras D(2,1;a),G(3),F(4) and the group gradings of Loop algebras and affine group scheme,the first aim is to determine the classifications of all group gradings and fine group gradings for exceptional simple modular Lie superalgebras D(2,1;a),G(3),F(4),respectively. ..2)By analogy of the classifications of all group gradings and fine group gradings for simple modular Cartan Lie algebras,according to the structures of simple modular Cartan Lie superalgebras W,S,H,K and the group gradings of Cayley algebras and affine group scheme,the second aim is to determine the classifications of all group gradings and fine group gradings for simple modular Cartan Lie superalgebras W,S,H,K,respectively. ..The classification of simple modular Lie superalgebras is not completed.The known simple modular Lie superalgebras play important roles. Then the classifications of group gradings for some simple modular Lie superalgebras are vital research topics.