The Hochschild cohomlogy ring of a self-injective Nakayama algebra is a Batalin-Vilkovisky algebra

TL;DR

This paper proves that the Hochschild cohomology ring of any self-injective Nakayama algebra always forms a Batalin-Vilkovisky algebra, extending previous results and correcting inaccuracies in the literature.

Contribution

It establishes that the BV algebra structure holds for all self-injective Nakayama algebras, removing the semisimplicity condition from prior results.

Findings

Hochschild cohomology ring of self-injective Nakayama algebra is a BV algebra

Corrects inaccuracies in existing literature

Extends BV algebra results to a broader class of algebras

Abstract

Lambre, Zhou and Zimmermann showed that the Hochschild cohomology ring of a Frobenius algebra with semisimple Nakayama automorphism is a Batalin-Vilkovisky algebra. They asked whether the semisimplicity condition is necessary. In this paper, we show that for a self-injective Nakayama algebra, the Hochschild cohomology ring is always a Batalin-Vilkovisky algebra. In course of proofs, we correct some inaccuracies in the literature, hoping not to introduce new errors.