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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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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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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Additional Information

Stephen F. Siegel
Affiliation: Department of Computer Science, University of Massachusetts, Amherst, Massachusetts 01003-4610
Email: siegel@cs.umass.edu

Sarah J. Witherspoon
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: withersp@math.wisc.edu

DOI: https://doi.org/10.1090/S0002-9939-00-05466-6
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