Hochschild Cohomology of Galois Coverings of Quantum Exterior Algebras
Received:June 11, 2012  Revised:February 19, 2013
Key Word: Hochschild cohomology   Galois covering   quantum exterior algebra.  
Fund ProjectL:The second author is supported by Beijing Natural Science Foundation (Grant No.1122006) and the National Natural Science Foundation of China (Grant No.11301144).
Author NameAffiliation
Jinmei FAN College of Science, Guilin University of Technology, Guangxi 541004, P. R. China 
Bo HOU School of Mathematics and Information Science, Henan University, Henan 475001, P. R. China 
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      In this paper, we consider the Hochschild cohomology of a class of quantum algebras $\Lambda_{\mathbbm{q}}^{n}$. We construct a minimal projective bimodule resolution of $\Lambda_{\mathbbm{q}}^{n}$, and calculate the $\k$-dimensions of all the Hochschild cohomology groups of $\Lambda_{\q}^{n}$. Furthermore, we give the Hochschild cohomology ring structure of $\Lambda_{\mathbbm{q}}^{n}$ for some special cases.
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