|
| 摘要: |
| 本文研究了特征零的代数闭域上秩为4 的有限维特殊Cartan 型李超代数S 的结构. 利用正则元的划分, 确定出S 关于典范环面的所有正根系, 从而得到了S 的所有Borel 子代数; 对于每一个正根系, 通过给出其单根系, 得到了任何两个Borel 子代数的连接关系; 最后确定了每一个Borel子代数的极大可解性. 本文所得结果可用于进一步研究Cartan 型单李超代数的结构与表示. |
| 关键词: 特殊Cartan型李超代数 正根系 Borel子代数 连接 |
| DOI： |
| 分类号:O151.2 |
| 基金项目:国家自然科学基金(11171055);黑龙江省杰出青年基金(JC201004). |
|
| BOREL SUBALGEBRAS OF SPECIAL LIE SUPERALGEBRAS OF CARTAN TYPE |
|
GAO Chun-yan,LIU Wen-de
|
| Abstract: |
| This article studies the structure of a finite-dimensional Special Lie superalgebra S of Cartan type of rank 4 over an algebraically closed field of characteristic zero. First, we characterize all the positive root systems with respect to the canonical torus by means of classifying all the regular elements and in particular we obtain all the Borel subalgebras with respect to the canonical torus. Second, we describe the connection relation between any two Borel subalgebras by means of determining the simple root system for every positive root system. Finally, we determine all the Borel subalgebras which are maximal solvable subalgebras. The main results can be used in the future for studying the structures and representations of the finite-dimensional Lie superalgebras of Cartan type. |
| Key words: special lie superalgebra of Cartan type positive root system Borel subalgebra connection |
