RESEARCH ARTICLE

Hochschild cohomology of n-Galois coverings of an algebra

  • Bo HOU , 1,2 ,
  • Jinmei FAN 3
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  • 1. School of Mathematics and Information Science, Henan University, Kaifeng 475001, China
  • 2. College of Applied Science, Beijing University of Technology, Beijing 100124, China
  • 3. College of Science, Guilin University of Technology, Guilin 541004, China

Received date: 20 Sep 2011

Accepted date: 16 Apr 2012

Published date: 01 Dec 2012

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

We consider the n-Galois covering Λn of the algebra A introduced by F. Xu [Adv. Math., 2008, 219: 1872-1893]. We calculate the dimensions of all Hochschild cohomology groups of Λn and give the ring structure of the Hochschild cohomology ring modulo nilpotence. As a conclusion, we provide a class of counterexamples to Snashall-Solberg’s conjecture.

Cite this article

Bo HOU , Jinmei FAN . Hochschild cohomology of n-Galois coverings of an algebra[J]. Frontiers of Mathematics in China, 2012 , 7(6) : 1113 -1128 . DOI: 10.1007/s11464-012-0215-4

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