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

JOURNAL OF ALGEBRA

卷:311

Article

Murray, John

关键词: green correspondence;    quadratic form;    symmetric bilinear form;    Frobenius-Schur indicator;    Broue-Robinson form;    Scott module;   

DOI  :  10.1016/j.jalgebra.2006.12.009

来源: Elsevier

【 摘 要 】

Let Phi be a principal indecomposable character of a finite group G in characteristic 2. The Frobenius-Schur indicator v(Phi) of Phi is shown to equal the rank of a bilinear form defined on the span of the involutions in G. Moreover, if the principal indecomposable module corresponding to Phi affords a quadratic geometry, then v(Phi) > 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. (c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

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