Murray, John
(2006)
Projective modules and involutions.
Journal of Alegbra, 299 (2).
pp. 616622.
ISSN 00218693
Abstract
Let $G$ be a finite group, and let $\Omega:=\{t\in G\mid t^2=1\}$. 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 $k\Omega$ is irreducible and selfdual, 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 $k\Omega$, establishes a bijection between the projective components of $k\Omega$ and the real $2$blocks of $G$ of defect zero.
Item Type: 
Article

Keywords: 
Projective Indecomposable Modules, Involutions 
Academic Unit: 
Faculty of Science and Engineering > Mathematics and Statistics 
Item ID: 
246 
Depositing User: 
Dr. John Murray

Date Deposited: 
30 Aug 2005 
Journal or Publication Title: 
Journal of Alegbra 
Publisher: 
Elsevier 
Refereed: 
No 
URI: 

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