$bv$-structure on the Hochschild cohomology algebra of local algebras of semidihedral type

A. I. Generalov, N. S. Zhamkov

Saint Petersburg State University (Saint Petersburg)

Abstract: We give a complete description of the $BV$-structure on the Hochschild cohomology for local algebras of semidihedral type over an algebraically closed field of characteristic $2$. In Erdmann's classification, these algebras are described by a parameter $k$. We consider the case of even parameter $k >3$. The methods of comparison morphisms and contracting homotopies are applied.

Keywords: Hochschild cohomology, homological algebra, Gerstenhaber bracket, Lie algebra, $BV$-structure.

UDC: 517

Received: 24.06.2025
Accepted: 17.10.2025

DOI: 10.22405/2226-8383-2025-26-4-88-97