李color代数的T^＊-扩张  

T^＊-Extension of Lie Color Algebras

作　　者：马瑶[1] 陈良云[1] 林洁[2] 

机构地区：[1]东北师范大学数学与统计学院,长春130024 [2]中国民航大学中欧航空工程师学院,天津300300

出　　处：《数学年刊（A辑）》2014年第5期623-638,共16页Chinese Annals of Mathematics

基　　金：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;吉林省自然科学基金(No.201115006)的资助

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.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. Moreoverl the equivalence of T^＊-extensions is investigated from the cohomological point of view.

关 键 词：T^＊-扩张 李color代数 幂零的 二次的 

分 类 号：O152.5[理学—数学]