一个自入射Koszul代数的Hochschild同调与循环同调
|
摘要
代数的Hochschild同调群与其对应的Gabriel箭图的循环圈有着紧密的联系.本文基于Furuya构造的一个四点自入射Koszul代数的极小投射双模分解,用组合的方法计算了该代数的Hochschild同调空间的维数,并用循环圈的语言给出该代数的Hochschild同调空间的一组k-基.进一步,当基础域k的特征为零时,我们也得到了该代数的循环同调群的维数.
There is a close connection between Hochschild homology groups of a kalgebra and cycles of the Gabriel quiver associated to the k-algebra. In this paper,based on the minimal projective bimodule resolution of a self-injective Koszul four-point algebra constructed by Furuya, we calculate the dimensions of Hochschild homology spaces of the algebra by using combinatorial methods, and give a k-basis of every Hochschild homology space in terms of cycles. Moreover, we obtain the dimensions of cyclic homology groups of the algebra when the base field k is of zero characteristic.
There is a close connection between Hochschild homology groups of a kalgebra and cycles of the Gabriel quiver associated to the k-algebra. In this paper,based on the minimal projective bimodule resolution of a self-injective Koszul four-point algebra constructed by Furuya, we calculate the dimensions of Hochschild homology spaces of the algebra by using combinatorial methods, and give a k-basis of every Hochschild homology space in terms of cycles. Moreover, we obtain the dimensions of cyclic homology groups of the algebra when the base field k is of zero characteristic.
引文
[1]Loday J.L.,Cyclic Homology,Grundlehren 301,Springer,Berlin,1992.
[2]Connes A.,Noncommutative differential geometry,IHES Publ.Math.,1985,62:257-360.
[3]Han Y.,Hochschild(co)homology dimension,J.London Math.Soc.,2006,73(2):657-668.
[4]Happel D.,Hochschild cohomology of finite dimensional algebras,Lecture Notes in Math.,1989,1404:108-126.
[5]Furuya T.,Hochschild cohomology for a class of self-injective special biserial algebras of rank four,J.Pure Appl.Algebra,2015,219:240 254.
[6]Xu Y.G.,Wang D.,Hochschild(co)homology of a class of Nakayama algebras,Acta Math.Sinica,2008,24(7):1097-1106.
[7]Liu S.X.,Zhang P.,Hoclischild homology of truncated algebras,Bull.London Math.Soc.,1994,26:427-430.
[2]Connes A.,Noncommutative differential geometry,IHES Publ.Math.,1985,62:257-360.
[3]Han Y.,Hochschild(co)homology dimension,J.London Math.Soc.,2006,73(2):657-668.
[4]Happel D.,Hochschild cohomology of finite dimensional algebras,Lecture Notes in Math.,1989,1404:108-126.
[5]Furuya T.,Hochschild cohomology for a class of self-injective special biserial algebras of rank four,J.Pure Appl.Algebra,2015,219:240 254.
[6]Xu Y.G.,Wang D.,Hochschild(co)homology of a class of Nakayama algebras,Acta Math.Sinica,2008,24(7):1097-1106.
[7]Liu S.X.,Zhang P.,Hoclischild homology of truncated algebras,Bull.London Math.Soc.,1994,26:427-430.