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

Part of: Representation theory of rings and algebras Homological methods

Published online by Cambridge University Press:  01 August 2008

HOU BO  and
XU YUNGE
HOU BO
Affiliation:
School of Mathematics and Computer Science, Hubei University, Wuhan 430062, PR China (email: bohou1981@163.com)
XU YUNGE*
Affiliation:
School of Mathematics and Computer Science, Hubei University, Wuhan 430062, PR China (email: xuy@hubu.edu.cn)
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Abstract

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Let Aq=k〈x,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.

Keywords

Hochschild (co)homologyquantum exterior algebraGalois covering

MSC classification

Secondary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.) 16G10: Representations of Artinian rings
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 1 , August 2008 , pp. 35 - 54
Copyright
Copyright © 2008 Australian Mathematical Society

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