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

Published online by Cambridge University Press:  01 August 2008

HOU BO
Affiliation:
School of Mathematics and Computer Science, Hubei University, Wuhan 430062, PR China (email: [email protected])
XU YUNGE*
Affiliation:
School of Mathematics and Computer Science, Hubei University, Wuhan 430062, PR China (email: [email protected])
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Abstract

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Let Aq=kx,y〉/(x2,xy+qyx,y2) be the quantum exterior algebra over a field k with , 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.

Type
Research Article
Copyright
Copyright © 2008 Australian Mathematical Society

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