| 特殊Cartan型李超代数的Borel子代数 |
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| 引用本文： | 高春艳,刘文德. 特殊Cartan型李超代数的Borel子代数[J]. 数学杂志, 2014, 34(6): 1170-1180 |
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| 作者姓名： | 高春艳 刘文德 |
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| 作者单位： | 哈尔滨师范大学数学科学学院; |
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| 基金项目： | 国家自然科学基金(11171055);黑龙江省杰出青年基金(JC201004) |
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| 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.
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| 关 键 词： | 特殊Cartan型李超代数 正根系 Borel子代数 连接 |
| 收稿时间： | 2013-11-26 |
| 修稿时间： | 2014-02-14 |
BOREL SUBALGEBRAS OF SPECIAL LIE SUPERALGEBRAS OF CARTAN TYPE |
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| GAO Chun-yan and LIU Wen-de. BOREL SUBALGEBRAS OF SPECIAL LIE SUPERALGEBRAS OF CARTAN TYPE[J]. Journal of Mathematics, 2014, 34(6): 1170-1180 |
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| Authors: | GAO Chun-yan and LIU Wen-de |
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| Affiliation: | School of Mathematical Sciences, Harbin Normal University, Harbin 150025, China and School of Mathematical Sciences, Harbin Normal University, Harbin 150025, China |
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| 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. |
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| Keywords: | special lie superalgebra of Cartan type positive root system Borel subalgebra connection |
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