| 马瑶,陈良云,林洁.李color代数的$T^*$-扩张[J].数学年刊A辑,2014,35(5):623~638 |
| 李color代数的$T^*$-扩张 |
| $T^*$-Extension of Lie Color Algebras |
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| DOI： |
| 中文关键词: $T^*$-扩张, 李color代数, 幂零的, 二次的 |
| 英文关键词:$T^*$-extension, Lie color algebra, Nilpotent, Quadratic |
| 基金项目:国家自然科学基金(No.11171055, No.11471090, No.11226054),
中央高校基本科研业务费专项资金(No.12SSXT139),
教育部留学回国人员科研启动基金和吉林省自然科学基金(No.201115006) |
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| 中文摘要: |
| 介绍了李color代数的$T^*$-扩张的定义, 并证明李color代数的很多性质, 如
幂零性、可解性和可分解性, 都可以提升到它的$T^*$-扩张上.
还证明在特征不等于2的代数闭域上, 有限维幂零二次李color代数$A$等距同构于一个幂零
李color代数$B$的$T^*$-扩张, 并且$B$的幂零长度不超过$A$的一半.
此外, 用上同调的方法研究了李color代数的$T^*$-扩张的等价类. |
| 英文摘要: |
| In this paper, the notion of $T^*$-extension of a Lie color algebra is introduced.
Many properties of a Lie color algebra can be lifted to its $T^*$-extensions,
such as nilpotency, solvability and decomposition.
It is proved that every finite-dimensional nilpotent quadratic Lie color algebra $A$
over an algebraically closed field of characteristic different from 2 is isometric to
a $T^{*}$-extension of a nilpotent Lie color algebra $B$,
and the nilpotent length of $B$ is at most half of that of $A$.
Moreover, the equivalence of $T^*$-extensions is investigated
from the cohomological point of view. |
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