# Koszul duality and the Hochschild cohomology of Artin-Schelter regular algebras

## TL;DR

This paper explores the relationship between Koszul duality and Hochschild cohomology of Artin-Schelter regular algebras, revealing connections between BV algebra structures in dual algebra pairs.

## Contribution

It establishes a link between two BV algebra structures on Hochschild cohomology for Koszul dual algebras with semisimple Nakayama automorphisms.

## Key findings

- Identification of two BV algebra structures on Hochschild cohomology
- Equivalence of these structures for Koszul dual pairs
- Extension of known structures to Artin-Schelter regular algebras

## Abstract

We identify two Batalin-Vilkovisky algebra structures, one obtained by Kowalzig and Krahmer on the Hochschild cohomology of an Artin-Schelter regular algebra with semisimple Nakayama automorphism and the other obtained by Lambre, Zhou and Zimmermann on the Hochschild cohomology of a Frobenius algebra also with semisimple Nakayama automorphism, provided that these two algebras are Koszul dual to each other.