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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 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. |
| Academic Unit: | Faculty of Science and Engineering > Mathematics and 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 |
| Related URLs: | |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/1788 |
| 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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