Gelfand-Ponamarev代数的Hochschild上同调群

Hochschild cohomology groups of Gelfand-Ponamarev algebra

设Λ=k〈x,y〉/(xy,yx,xs,yt),s,t>1为代数闭域k上的Gelfand-Ponamarev代数.基于Bardzell对零关系代数的极小投射双模分解的细致分析,代数Λ的极小投射双模分解被清晰构造,进而Λ的各阶Hochschild上同调群的维数被准确地计算.

Let А=κ（z,y）/（xy,yx,x′,y′）,s,t〉1 be the Gelfand-Ponamarev algebra over algebraically closed field k. Using Bardzell＇s method, the minimal projective bimodule sesolution of A is construsted, then the dimensions of Hochschild cohomology groups of A are explicitly calculated.