$BV$-structure on Hochschild cohomology for exceptional local algebras of quaternion type. Case of even parameter

TL;DR

This paper fully describes the Batalin-Vilkovisky (BV) structure on the Hochschild cohomology of certain quaternion-type local algebras with even parameters, extending previous results in the field.

Contribution

It provides a comprehensive analysis of the BV-structure for exceptional local algebras of quaternion type with even parameters, using comparison morphisms and weak self-homotopy methods.

Findings

Explicit description of BV-structure for these algebras

Generalization of previous results on quaternion type algebras

Development of new methods for analyzing Hochschild cohomology

Abstract

We give a full description of the $BV$-structure on the Hochschild cohomology of exceptional local algebras of quaternion type, defined by parameters $(k,0,d)$ in case of even parameter $k \geqslant 3$, according to Erdmann's classification. We develop and use the method of comparison morphisms and weak self-homotopy method. This article states as a generalization of similar results about $BV$-structures on Hochscild cohomology of algebras of quaternion type.