RESEARCH ARTICLE

Hochschild cohomology ring modulo nilpotence of a one point extension of a quiver algebra defined by two cycles and a quantum-like relation

  • Daiki OBARA
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  • Department of Mathematics, Tokyo University of Science, Shinjuku-ku, Tokyo, Japan

Received date: 27 Oct 2015

Accepted date: 23 Feb 2016

Published date: 30 Aug 2016

Copyright

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

We consider a one point extension algebra B of a quiver algebra Aq over a field k defined by two cycles and a quantum-like relation depending on a nonzero element q in k. We determine the Hochschild cohomology ring of B modulo nilpotence and show that if q is a root of unity, then B is a counterexample to Snashall-Solberg’s conjecture.

Cite this article

Daiki OBARA . Hochschild cohomology ring modulo nilpotence of a one point extension of a quiver algebra defined by two cycles and a quantum-like relation[J]. Frontiers of Mathematics in China, 2016 , 11(4) : 1003 -1015 . DOI: 10.1007/s11464-016-0553-8

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