| 林洁,陈良云,汪金燕.关于可解李三超系[J].数学年刊A辑,2009,30(4):505~516 |
| 关于可解李三超系 |
| On Solvable Lie Triple Supersystems |
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| DOI： |
| 中文关键词: 李三超系 标准嵌入李超代数 T-可解 T-幂零 不变双线性型 |
| 英文关键词:Lie triple supersystem, The standard imbedding Lie superalgebra,
T -Solvable, T -Nilpotent, Invariant bilinear form |
| 基金项目:国家自然科学基金(No.10701019;No.10871057)资助的项目.和帮助 |
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| 中文摘要: |
| 给出了关于李三超系的一些基本概念和性质,包括:(1)可解李三超系的任意包络李超代数都是可解的;(2)如果一个李蔓超系有可解的包络李超代数,则它也是可解的;(3)一个李三超系T是幂零的当且仅当它的标准嵌入李超代数L(T)是幂零的;(4)L(T)的中心等于T的中心;(5)李三超系上的右不变超对称双线性型可唯一地扩张到它的标准嵌入李超代数上. |
| 英文摘要: |
| The authors give some elementary concepts and properties on Lie triple super-
systems, including: (1) Any enveloping Lie superalgebra of a solvable Lie triple supersystem
is solvable; (2) If a Lie triple supersystem has some solvable enveloping Lie superalgebra,
then it is solvable; (3) A Lie triple supersystem T is nilpotent if and only if its standard
imbedding Lie superalgebra L(T ) is nilpotent; (4) The center of L(T ) is equal to that of
T ; (5) A right-invariant supersymmetric bilinear form on a Lie triple supersystem can be
uniquely extended on its standard imbedding Lie superalgebra. |
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