BV-structure on Hochschild cohomology for exeptional local algebras of quaternion type: case of even dimension

We give BV-structures full description for case of even dimension $k ge 3$ on Hochschild cohomology for exeptional local algebras of quaternion type, defined by parameters $(0,d)$, according to Erdmann classification. This article states as a generalization of similar results about $BV$-structures on quaternion type algebras.