No abstract

We define a cup product on the Hochschild cohomology of an associative conformal algebra A, and show the cup product is graded commutative. We define a graded Lie bracket with the degree −1 on the Hochschild cohomology HH * (A) of an associative conformal algebra A, and show that the Lie bracket together with the cup product is a Gerstenhaber algebra on the Hochschild cohomology of an associative conformal algebra. Moreover, we consider the Hochschild cohomology of split extension conformal algebra A ⊕M of A with a conformal bimodule M, and show that there exist an algebra homomorphism from HH * (A ⊕M) to HH * (A).