Projective indecomposable modules, Scott modules and the Frobenius–Schur indicator
- 作者：John Murray
- 关键词：Green correspondence ; Quadratic form ; Symmetric bilinear form ; Frobenius– ; Schur indicator ; Broué ; – ; Robinson form ; Scott module
- 刊名：Journal of Algebra
- 出版年：2007
- 期刊代码：69_00218693
- 类别：mt
- 出版时间：15 May 2007
- 卷：311
- 期：2
- 页码：800-816
- 文件大小：216 K
摘要
Let Φ be a principal indecomposable character of a finite group G in characteristic 2. The Frobenius–Schur indicator ν(Φ) of Φ 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 Φ affords a quadratic geometry, then ν(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.