Murray, John (2006) Projective modules and involutions. Journal of Alegbra, 299 (2). pp. 616-622. ISSN 0021-8693

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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 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 $k\Omega$, 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:	http://www.maths.may.ie/staff/jmurray/my... http://www.sciencedirect.com/science/jou...
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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