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Projective indecomposable modules, Scott modules and the Frobenius-Schur indicator

Murray, John (2007) Projective indecomposable modules, Scott modules and the Frobenius-Schur indicator. Journal of Alegbra, 311 (2). pp. 800-816. ISSN 0021-8693

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Let Φ be a principal indecomposable character of a fi nite group G in characteristic 2. The Frobenius-Schur indicator v(Φ) of Φ is shown to equal the rank of a bilinear form de ned on the span of the involutions in G. Moreover, if the principal indecomposable module corresponding to Φ aff ords a quadratic geometry, then v(Φ) > 0. This result is used to prove a more precise form of a theorem of Benson and Carlson on the existence of Scott components in the endomorphism ring of an indecomposable G-module, in case the module aff ords a G-invariant symmetric form.

Item Type: Article
Keywords: Green correspondence; Quadratic form; Symmetric bilinear form; Frobenius–Schur indicator; Broué–Robinson form; Scott module.
Subjects: Science & Engineering > Mathematics & Statistics
Item ID: 1788
Identification Number: 10.1016/j.jalgebra.2006.12.009
Depositing User: Dr. John Murray
Date Deposited: 30 Mar 2010 10:04
Journal or Publication Title: Journal of Alegbra
Publisher: Elsevier - Academic Press
Refereed: No

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