HOCHSCHILD (CO)HOMOLOGY OF ℤ2×ℤ2-GALOIS COVERINGS OF QUANTUM EXTERIOR ALGEBRAS

Let Aq=k〈x,y〉/(x2,xy+qyx,y2) be the quantum exterior algebra over a field k with $\mathrm {char}\,k\neq 2$, and let Λq be the ℤ2×ℤ2-Galois covering of Aq. In this paper the minimal projective bimodule resolution of Λq is constructed explicitly, and from it we can calculate the k-dimensions of all Hochschild homology and cohomology groups of Λq. Moreover, the cyclic homology of Λq can be calculated in the case where the underlying field is of characteristic zero.