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

The case of small parameter. This is the second paper in the cycle of papers about the $BV$-structure on the Hocshild cohomology of exceptional algebras of quaternion type. The full description of the $BV$-structure is given for the case of algebras $R(k,0,d)$ of quaternion type, defined by parameter $k = 2$ according to the Erdmann classification.