BV structure on the Hochschild cohomology of Liu-Schulz algebras in characteristic two

Abstract

Let $K$ be a field of characteristic $2$, let $ρ\in K^\times$, and let $R_ρ$ be the corresponding Liu-Schulz algebra. We give a complete description of the Gerstenhaber bracket and the BV structure on the Hochschild cohomology ring $\operatorname{HH}^*(R_ρ)$.