The Hochschild cohomology ring of a cyclic block

Siegel, Stephen; Witherspoon, Sarah

doi:10.1090/S0002-9939-00-05466-6

The Hochschild cohomology ring of a cyclic block
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by Stephen F. Siegel and Sarah J. Witherspoon PDF

Proc. Amer. Math. Soc. 128 (2000), 1263-1268 Request permission

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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