The Hochschild cohomology ring of a cyclic block

Abstract

Suppose B B is a block of a group algebra k G kG with cyclic defect group. We calculate the Hochschild cohomology ring of B B , giving a complete set of generators and relations. We then show that if B B is the principal block, the canonical map from H ∗ ( G , k ) H^*(G,k) to the Hochschild cohomology ring of B B induces an isomorphism modulo radicals.