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

TL;DR

This paper fully describes the Batalin-Vilkovisky (BV) structure on the Hochschild cohomology of specific quaternion type algebras, focusing on the case where the parameter k equals 2, advancing understanding of algebraic structures.

Contribution

It provides a complete description of the BV-structure on Hochschild cohomology for quaternion algebras R(2,0,d), a case previously not fully understood.

Findings

Explicit BV-structure formulas for R(2,0,d)

Advancement in classification of Hochschild cohomology for quaternion algebras

Enhanced understanding of algebraic structures in quaternion type algebras

Abstract

This is the second paper in the cycle of articles about $BV$-structure on Hochshild cohomology of exceptional algebras of quaternion type. We give $BV$-structure's full description in the case of quaternion algebras $R(k,0,d)$, defined by parameter $k = 2$ according to Erdmann classification.