minimal projective bimodule resolution
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2008 ◽  
Vol 78 (1) ◽  
pp. 35-54
Author(s):  
HOU BO ◽  
XU YUNGE

AbstractLet 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.


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