二元外代数的Z_n-Galois覆盖代数的Hochschild(上)同调群

Hochschild (Co)-Homology Groups of Zn-Galois Coverings of Exterior Algebras in Two Variables

设Λ是特征不整除n的域k上的二元外代数,■是Λ的Zn-Galois覆盖代数.首先构造了■的极小投射双模分解,并由此清晰地计算了■的各阶Hochschild同调和上同调群的维数;并且在域的特征为零时,计算了■的循环同调群的维数.

Let Λ be the exterior algebras in two variables over a field k satisfying chark ＋ n, Λ^~ be the Zn-Galois covering of Λ. We construct a minimal projective bimodule resolution of Λ^~, and then we can explicitly calculate the Hochschild homology and co-homology of Λ^~. Moreover, the cyclic homology of Λ^~ can be calculated in case the underlying field is of characteristic zero.