Leibniz超代数和Hom-Leibniz超代数的非交换张量积

发布时间：2018-02-23 02:23

本文关键词： Leibniz超代数 Hom-Leibniz超代数 Leibniz作用 Hom-Leibniz作用半直积同调非交换张量积　出处：《东北师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文定义了Leibniz超代数的Leibniz作用,半直积和交叉模,总结出Leibniz超代数的同调及一些低维同调结果,随后构造并定义了Leibniz超代数的非交换张量积,进而研究其相关性质,获得了以上概念的一些重要结果.又进一步将Leibniz超代数进行推广,探讨了Hom-Leibniz超代数的Hom-Leibniz作用,通过探究与验证,定义了这个代数的半直积和交叉模以及Hom-Leibniz超代数的非交换张量积,获得了相关重要性质.本文丰富了Leibniz超代数和Hom-Leibniz超代数的理论内容,为研究其它代数的非交换张量积起到了重要作用,促进了Leibniz代数的发展.
[Abstract]:In this paper, the Leibniz action, semidirect product and cross modules of Leibniz superalgebras are defined. The homology of Leibniz superalgebras and some low-dimensional homology results are summarized. Then, the noncommutative tensor product of Leibniz superalgebras is constructed and defined, and the related properties of Leibniz superalgebras are studied. Some important results of the above concepts are obtained. Furthermore, the Leibniz superalgebras are generalized, and the Hom-Leibniz function of Hom-Leibniz superalgebras is discussed. The semidirect product and cross module of this algebra and the noncommutative tensor product of Hom-Leibniz superalgebra are defined, and the related important properties are obtained. The theoretical contents of Leibniz superalgebra and Hom-Leibniz superalgebra are enriched in this paper. It plays an important role in studying the noncommutative tensor product of other algebras and promotes the development of Leibniz algebras.
【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

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