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