一个cluster-tilted代数的Hochschild上同调环

发布时间：2018-07-01 16:59

本文选题：cluster-tilted代数 + Hochschild上同调环　；参考：《湖北大学》2015年硕士论文

【摘要】：Hochschild上同调理论是由Hochschild引入,由Cartan和Eilenberg发展并逐步完善的一个同调代数分支,在代数的表示理论中扮演着十分重要的角色。有限维代数的Hochschild上同调空间关于cup积作成一个分次交换环。本文研究了一个特殊的cluster-tilted代数的Hochschild上同调环的结构。该代数是特殊双列Koszul非自入射代数。本文首先基于Furuya构造的极小投射双模分解,定义了该投射分解的所谓“余乘”结构,从而证明了该代数的Hochschild上同调的cup积本质上是平行路的毗连。由此,我们进一步得到了该代数的Hochschild上同调环的一个由生成元与关系给出的实现。
[Abstract]:The Hochschild homology theory is a branch of the homology algebra introduced by Hochschild, developed and perfected by Cartan and Eilenberg, and plays a very important role in the representation theory of algebra. The homology space on the Hochschild of the finite dimensional algebra is made into a sub exchange ring on the cup product. In this paper, a special cluster-ti is studied. The structure of the homology ring on the Hochschild of the lted algebra. This algebra is a special double column Koszul non self incident algebra. This paper first defines the so-called "residual multiplicative" structure of the projective decomposition based on the minimal projection dual-mode decomposition of the Furuya construction. Thus, it is proved that the cup product of the homology on the Hochschild of the algebra is essentially contiguous to the parallel path. We further get the realization of a generator and relation on the Hochschild cohomology ring of the algebra.
【学位授予单位】：湖北大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O154.2

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