Group Representations, Part 2
This second volume deals with projective representations and the Schur multiplier. Some further topics pertaining to projective representations will be covered in the next volume. The bibliography is extensive, leading the reader to various references for detailed discussions on the main topics as well as on related subjects.
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Projective Representations I
Twisted Group Algebras
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abelian group acts trivially algebraically closed field arbitrary field central extension char F coboundary cocycle cohomology class commutative conjugacy classes covering group cyclic cyclic group deduce defined denotes desired conclusion divide G elementary abelian elements equivalent exact sequence exists F-algebra F*G-modules field of characteristic finite group FºC Fºg free group G act G and let g e G G over F given GL(V group algebra group and let group G h e H H-module Hence Hom(A Hom(G Hom(N induced integer irreducible isomorphism Lemma Let F Let G let H let o e module nilpotent nilpotent group normal subgroup o e Zº(G o-regular o-representation p-group projective representations Proposition prove representation of G result follows RG-module Schur multiplier simple subgroup of G suffices to show surjective Sylow p-subgroup twisted group algebra ye G ZºCG