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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 |
| Related URLs: | |
| 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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