More counterexamples to Happel's question and Snashall-Solberg's conjecture

Abstract

In this paper we provide more counterexamples to Happel's question and Snashall-Solberg's conjecture which generalize many counterexamples to these conjectures studied in the literature. In particular, we show that a family of ${\mathbb{Z}}_n\times {\mathbb{Z}}_n$-Galois covering algebras of quantized exterior algebra $A_q$ in two variables answer negatively to Happel's question, and meanwhile, the one-point coextensions of ${\mathbb{Z}}_n$ and ${\mathbb{Z}}_n\times {\mathbb{Z}}_m$-Galois covering algebras of $A_q$ negate the Snashall-Solberg's conjecture.

20 pages

References in corpus (3)

• Multiplicative structures for Koszul algebras
• Support varieties and the Hochschild cohomology ring modulo nilpotence
• A family of Koszul self-injective algebras with finite Hochschild cohomology

Cited by in corpus (2)

• Centers of partly (anti-)commutative quiver algebras and finite generation of the Hochschild cohomology ring
• Cup product on Hochschild cohomology of a family of quiver algebras