Hom-李color代数和完美李color代数的线性变换的若干性质
发布时间：2018-09-07 20:33
【摘要】：本论文的主要内容分成两部分.第一部分研究了特征不等于2的完美李color代数的两类线性变换:三导子和三同态,证明了完美李color代数的三导子都是它的导子,导子代数的三导子都是它的内导子,同时给出了完美李color代数的一个三同态是同态、反同态、同态与反同态的和的必要条件.第二部分研究了Hom-李color代数的六类线性变换:型心、拟型心、导子、中心导子、拟导子、广义导子.我们证明了中心导子代数是导子代数的Hom-理想,型心是导子代数的理想,以及一个中心为0的Hom-李color代数的拟型心是交换的,当且仅当它是一个Hom-李color代数.其次证明了广义导子代数等于拟导子代数和拟型心的和,最后证明了拟导子代数可以嵌入到一个比它更大的Hom-李color代数的导子代数中.
[Abstract]:The main content of this paper is divided into two parts. In the first part, we study two kinds of linear transformations of perfect lie color algebras whose characteristic is not equal to 2: three derivations and three homomorphisms. It is proved that the three derivations of perfect lie color algebras are its derivations, and the three derivations of derivation algebras are its inner derivations. A necessary condition for the sum of homomorphism, anti-homomorphism, homomorphism and anti-homomorphism of a perfect lie color algebra is also given. In the second part, we study six kinds of linear transformations of Hom- lie color algebras: type center, quasi type center, derivation, center derivation, quasi derivation and generalized derivation. We prove that the central derivation algebra is the Hom- ideal of the derivation algebra, the type center is the ideal of the derivation algebra, and the quasi-type center of a Hom- lie color algebra with center 0 is commutative if and only if it is a Hom- lie color algebra. Secondly, it is proved that the generalized derivation algebra is equal to the sum of the quasi derivation algebra and the quasi type center. Finally, it is proved that the quasi derivation algebra can be embedded into the derivation algebra of a Hom- lie color algebra larger than it.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O152.5
本文编号：2229341
[Abstract]:The main content of this paper is divided into two parts. In the first part, we study two kinds of linear transformations of perfect lie color algebras whose characteristic is not equal to 2: three derivations and three homomorphisms. It is proved that the three derivations of perfect lie color algebras are its derivations, and the three derivations of derivation algebras are its inner derivations. A necessary condition for the sum of homomorphism, anti-homomorphism, homomorphism and anti-homomorphism of a perfect lie color algebra is also given. In the second part, we study six kinds of linear transformations of Hom- lie color algebras: type center, quasi type center, derivation, center derivation, quasi derivation and generalized derivation. We prove that the central derivation algebra is the Hom- ideal of the derivation algebra, the type center is the ideal of the derivation algebra, and the quasi-type center of a Hom- lie color algebra with center 0 is commutative if and only if it is a Hom- lie color algebra. Secondly, it is proved that the generalized derivation algebra is equal to the sum of the quasi derivation algebra and the quasi type center. Finally, it is proved that the quasi derivation algebra can be embedded into the derivation algebra of a Hom- lie color algebra larger than it.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O152.5
【参考文献】
相关期刊论文 前2条
1 陈良云;;Hom-李型代数的若干结果[J];四川师范大学学报(自然科学版);2017年02期
2 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年05期
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