二元外代数的Z_2×Z_2-Galois覆盖代数的Hochschild(上)同调群

Hochschild(co)homology groups of Z_2×Z_2-Galois covering of exterior algebra in two variables

设∧是特征不整除4的域k上的二元外代数，五是以的Z2×Z2-Galois覆盖代数．利用组合的方法，覆盖代数∧的各阶Hochschild（上）同调群的维数被清晰地计算，并且在域k的特征为零时，五的各阶循环同调群的维数也被给出．

Let A be the exterior algebra in two variabls over a field k with chark 4, ∧ be theZ2×Z2-Galois covering of ∧. The dimensions of Hochschild homology and cohomology groups of ∧ arecalculated in terms of combinatorics. Moreover, the dimensions of cyclic homology groups of ∧ can be calculated when the characteristic of the underlying field k is zero.