Hochschild Cohomology of Quiver Algebras Defined by Two Cycles and a Quantum-Like Relation II

Abstract

We consider quiver algebras A _q 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 A _q and give necessary and sufficient conditions for A _q to have the finitely generated Hochschild cohomology ring.

Key Words:

• Finiteness conditions
• Hochschild cohomology
• Quantum-like relation

AMS 2010 Mathematics Subject Classication:

• 16E40
• 16G20

ACKNOWLEDGMENT

The author is grateful to Professor Katsunori Sanada and Dr. Takahiko Furuya for many valuable comments and suggestions.

Notes

Communicated by D. Zacharia.

¹The first part of this article can be read in Communication in Algebra, Vol. 40, pp. 1724–1761, reference [14] in this article.