| 一个Cluster-Tilted代数的Hochschild上同调环 |
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| 引用本文： | 徐运阁,赵体伟,吴迪.一个Cluster-Tilted代数的Hochschild上同调环[J].数学学报,2016,59(4):505-518. |
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| 作者姓名： | 徐运阁 赵体伟 吴迪 |
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| 作者单位： | 1. 湖北大学数学与统计学学院 武汉 430062;
2. 南京大学数学系 南京 210093 |
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| 基金项目： | 国家自然科学基金资助项目(11371186,11571341) |
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| 摘 要： | 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.
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| 关 键 词： | cluster-tilted代数 cup积 Hochschild上同调环 平行路 |
Hochschild Cohomology Ring of a Cluster-Tilted Algebra |
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| Yun Ge XU,Ti Wei ZHAO,Di WU.Hochschild Cohomology Ring of a Cluster-Tilted Algebra[J].Acta Mathematica Sinica,2016,59(4):505-518. |
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| Authors: | Yun Ge XU Ti Wei ZHAO Di WU |
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| Institution: | 1. Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, P. R. China;
2. Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China |
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| Abstract: | 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. |
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| Keywords: | cluster-tilted algebra cup product Hochschild cohomology ring parallel path |
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