| 李color代数的T~*-扩张 |
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| 引用本文： | 马瑶,陈良云,林洁. 李color代数的T~*-扩张[J]. 数学年刊A辑(中文版), 2014, 35(5): 623-638 |
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| 作者姓名： | 马瑶 陈良云 林洁 |
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| 作者单位： | 东北师范大学数学与统计学院, 长春 130024.;东北师范大学数学与统计学院, 长春 130024.;中国民航大学中欧航空工程师学院, 天津 300300. |
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| 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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| 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.
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| 关 键 词： | $T^*$-扩张 李color代数 幂零的 二次的 |
$T^*$-Extension of Lie Color Algebras |
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| MA Yao,CHEN Liangyun and LIN Jie. $T^*$-Extension of Lie Color Algebras[J]. Chinese Annals of Mathematics, 2014, 35(5): 623-638 |
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| Authors: | MA Yao CHEN Liangyun LIN Jie |
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| Affiliation: | School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China.;School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China.;Sino-European Institute of Aviation Engineering, Civil Aviation University of China, Tianjin 300300, China. |
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| Abstract: | 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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| Keywords: | $T^*$-extension Lie color algebra Nilpotent Quadratic |
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