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The Hochschild Cohomology Ring of a Group Algebra
Author(s) -
Siegel Stephen F.,
Witherspoon Sarah J.
Publication year - 1999
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611599011958
Subject(s) - mathematics , cohomology ring , cohomology , group cohomology , ring (chemistry) , group (periodic table) , conjugacy class , group ring , dihedral group , pure mathematics , cup product , finite group , group algebra , algebra over a field , equivariant cohomology , de rham cohomology , chemistry , organic chemistry
There is a standard additive decomposition of the Hochschild cohomology ring of the group algebra of a finite group G as the direct sum of the cohomology rings of the centralizers of representatives of the conjugacy classes of G . A special case of our main result describes the cup product in terms of this decomposition. As applications, we determine presentations for the Hochschild cohomology rings of [(1)] the mod‐3 group algebra of the symmetric group S 3 , [(2)] the mod‐2 group algebra of the alternating group A 4 , and [(3)] the mod‐2 group algebras of the dihedral 2‐groups. 1991 Mathematics Subject Classification : 16E40, 20J06.