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    Projective modules and involutions

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

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    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
    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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