一个Cluster-Tilted代数的Hochschild上同调环
Hochschild Cohomology Ring of a Cluster-Tilted Algebra
基于Furuya构造的一个cluster-tilted代数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上同调环的cup积本质上是平行路的毗连并由此得到了该代数的Hochschild上同调环的一个由生成元与关系给出的实现.
In this paper, based on the minimal projective bimodule resolution of a cluster-tilted algebra given by Furuya, we define the so-called "comultiplication" structure of the minimal projective bimodule resolution, and show that the cup product of Hochschild cohomology ring of the cluster-tilted algebra is essentially juxtaposition of parallel paths up to sign. As a consequence, we determine the structure of the Hochschild cohomology ring under the cup product by giving an explicit presentation via generators and relations.
cluster-tilted代数 / cup积 / Hochschild上同调环 / 平行路 {{custom_keyword}} /
cluster-tilted algebra / cup product / Hochschild cohomology ring / parallel path {{custom_keyword}} /
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国家自然科学基金资助项目(11371186,11571341)
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