几类有限维代数的低阶Hochschild上同调群  

Low-order Hochschild Cohomology Groups of Several Finite Dimensional Algebras

作　　者：李艳凤[1] 刘海成[1] 朱桂英[1] Li Yanfeng;Liu Haicheng;Zhu Guiying(College of Science,Heilongjiang Bayi Agricultural Univercity,Daqing 163319)

机构地区：[1]黑龙江八一农垦大学理学院

出　　处：《黑龙江八一农垦大学学报》2019年第3期120-124,共5页journal of heilongjiang bayi agricultural university

基　　金：黑龙江八一农垦大学博士科研启动基金(XDB-2016-25)

摘　　要：自1945 年Hochschild 提出有限维代数的Hochschild 上同调群以来,经大家深入的研究和整理,在数学的很多领域得到了广泛的应用和推广,如Lie 代数,代数表示论,代数拓扑等等。一般来说,结合代数的Hochschild 上同调群与它的代数结构之间有着紧密的联系,特别是对于一些低阶的Hochschild上同调群,零阶为代数的中心,一阶为结合代数的外导子。所以,各种代数的Hochschild 上同调群的计算在代数及其表示论中有着重要意义。Since Hochschild proposed the Hochschild cohomology group of finite dimensional algebra in 1945,after deep research and arrangement,it was widely applied in many fields of mathematics,such as Lie algebra,algebraic representation theory,algebraic topology and so on. Generally,there was a close relationship between the Hochschild cohomology groups and the algebraic structure of associative algebra.Especially for some low-order Hochschild cohomology groups,the zero order was the center of algebra and the first order was the outer derivations of associative algebra.Therefore,the computation of Hochschild cohomology groups in various algebras played an important role in algebra and its representation theory. According to the characteristics of double modules in finite dimensional algebra and the theory of Hochschild cohomology group.

关 键 词：HOCHSCHILD 上同调群 有限维代数 结合代数 

分 类 号：O154.2[理学—数学]