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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Abstract

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 affords 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 affords a G-invariant symmetric form.

Item Type:	Article
Keywords:	Green correspondence; Quadratic form; Symmetric bilinear form; Frobenius–Schur indicator; Broué–Robinson form; Scott module.
Academic Unit:	Faculty of Science and Engineering > Mathematics and Statistics
Item ID:	1788
Identification Number:	https://doi.org/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
URI:	Publisher
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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