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