Hochschild Cohomology of q-Schur Algebras

We compute the Hochschild cohomology of any block of q -Schur algebras. We focus on the even part of this Hochschild cohomology ring. To compute the Hochschild cohomology of q -Schur algebras, we prove the following two results: first, we construct two graded algebra surjections between the Hochschild cohomologies of quasi-hereditary algebras because all q -Schur algebras over a field are quasi-hereditary. Second, we give the graded algebra isomorphism of Hochschild cohomologies by using a certain derive equivalence.