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

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