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The Hochschild cohomology ring of a cyclic block

Authors: Stephen F. Siegel and Sarah J. Witherspoon
Journal: Proc. Amer. Math. Soc. 128 (2000), 1263-1268
MSC (2000): Primary 20J06, 16E40
Published electronically: February 7, 2000
MathSciNet review: 1691003
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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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Additional Information

Stephen F. Siegel
Affiliation: Department of Computer Science, University of Massachusetts, Amherst, Massachusetts 01003-4610

Sarah J. Witherspoon
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706

Keywords: Finite groups, representation theory, Hochschild cohomology, blocks, cyclic defect
Received by editor(s): March 15, 1998
Published electronically: February 7, 2000
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 2000 American Mathematical Society