一个Cluster-Tilted代数的Hochschild同调与循环同调
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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,用组合的方法计算了Cluster-Tilted代数的Hochschild同调空间的维数与基.当基础域的特征为零时,也计算了代数的循环同调群的维数.
In this paper,based on the minimal projective bimodule resolution of a clustertilted algebra constructed by Furuya,we calculate the dimensions and bases of all the Hochschild homology spaces of a cluster-tilted algebra by using combinatorial methods.When the characteristic of the ground field k is zero,we also compute the dimensions of cyclic homology groups.
In this paper,based on the minimal projective bimodule resolution of a clustertilted algebra constructed by Furuya,we calculate the dimensions and bases of all the Hochschild homology spaces of a cluster-tilted algebra by using combinatorial methods.When the characteristic of the ground field k is zero,we also compute the dimensions of cyclic homology groups.
引文
[1]Hochschild G,Kostant B,Rosenberg A.Differential forms on regular affine algebtas[J].Transactions AMS,1962,102(3):383-408.
[2]Loday J L.Cyclic homology[M].Grundlehren,301,Springer,Berlin,1992.
[3]Connes A.Noncommutative differential geometry[J].IHES Publ.Math,1985(62):257-360.
[4]Han Y.Hochschild(co)homology dimension[J].London Math Soc,2006,73(2):657-668.
[5]Happel D.Hochschild cohomology of finite dimensional algebras[J].Lecture Notes in Math,1989,1404:108-126.
[6]Xu Y G,Wang D.Hochschild(co)homology of a class of Nakayama algebras[J].Acta Math Sinica,2008,24(1),1097-1106.
[7]Liu S X,Zhang P.Hochschild homology of truncated algebras[J],Bull.London Math Soc,1994,26:427-430.
[8]Bastian J,Holm T,Ladkani S.Towards derived equivalence classification of the cluster-tilted algebras of Dynkin type D[J].J Algebra,2014,410:277-332.
[9]Furuya T.A projective bimodule resolution and the Hochschild cohomology for a cluster-tilted algebra of type D_4[J].SUT Journal of Mathematics,2012,48:145-169.
[10]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.
[2]Loday J L.Cyclic homology[M].Grundlehren,301,Springer,Berlin,1992.
[3]Connes A.Noncommutative differential geometry[J].IHES Publ.Math,1985(62):257-360.
[4]Han Y.Hochschild(co)homology dimension[J].London Math Soc,2006,73(2):657-668.
[5]Happel D.Hochschild cohomology of finite dimensional algebras[J].Lecture Notes in Math,1989,1404:108-126.
[6]Xu Y G,Wang D.Hochschild(co)homology of a class of Nakayama algebras[J].Acta Math Sinica,2008,24(1),1097-1106.
[7]Liu S X,Zhang P.Hochschild homology of truncated algebras[J],Bull.London Math Soc,1994,26:427-430.
[8]Bastian J,Holm T,Ladkani S.Towards derived equivalence classification of the cluster-tilted algebras of Dynkin type D[J].J Algebra,2014,410:277-332.
[9]Furuya T.A projective bimodule resolution and the Hochschild cohomology for a cluster-tilted algebra of type D_4[J].SUT Journal of Mathematics,2012,48:145-169.
[10]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.