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Projective modules and involutions | | John Murray
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23 Mar 2004 | | Subject: | Representation Theory; Group Theory MSC-class: 20C20 | math.RT math.GR | | Abstract: | Let G be a finite group, and let Omega:={tin Gmid t^2=1}. Then Omega is a G-set under conjugation. Let k be an algebraically closed field of characteristic 2. It is shown that each projective indecomposable summand of the G-permutation module kOmega is irreducible and self-dual, whence it belongs to a real 2-block of defect zero. This, together with the fact that each irreducible kG-module that belongs to a real 2-block of defect zero occurs with multiplicity 1 as a direct summand of kOmega, establishes a bijection between the projective components of kOmega and the real 2-blocks of G of defect zero. | | Source: | arXiv, math.RT/0403388 | | Services: | Forum | Review | PDF | Favorites | |
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