A filtration of the modular representation functor
| dc.citation.epage | 179 | en_US |
| dc.citation.issueNumber | 1 | en_US |
| dc.citation.spage | 140 | en_US |
| dc.citation.volumeNumber | 318 | en_US |
| dc.contributor.author | Yaraneri, E. | en_US |
| dc.date.accessioned | 2016-02-08T10:11:24Z | |
| dc.date.available | 2016-02-08T10:11:24Z | |
| dc.date.issued | 2007 | en_US |
| dc.department | Department of Mathematics | en_US |
| dc.description.abstract | Let F and K be algebraically closed fields of characteristics p > 0 and 0, respectively. For any finite group G we denote by K RF (G) = K ⊗Z G0 (F G) the modular representation algebra of G over K where G0 (F G) is the Grothendieck group of finitely generated F G-modules with respect to exact sequences. The usual operations induction, inflation, restriction, and transport of structure with a group isomorphism between the finitely generated modules of group algebras over F induce maps between modular representation algebras making K RF an inflation functor. We show that the composition factors of K RF are precisely the simple inflation functors SC, Vi where C ranges over all nonisomorphic cyclic p′-groups and V ranges over all nonisomorphic simple K Out (C)-modules. Moreover each composition factor has multiplicity 1. We also give a filtration of K RF. © 2007 Elsevier Inc. All rights reserved. | en_US |
| dc.identifier.doi | 10.1016/j.jalgebra.2007.06.030 | en_US |
| dc.identifier.eissn | 1090-266X | |
| dc.identifier.issn | 0021-8693 | |
| dc.identifier.uri | http://hdl.handle.net/11693/23283 | |
| dc.language.iso | English | en_US |
| dc.publisher | Academic Press | en_US |
| dc.relation.isversionof | http://dx.doi.org/10.1016/j.jalgebra.2007.06.030 | en_US |
| dc.source.title | Journal of Algebra | en_US |
| dc.subject | (Global) Mackey functor | en_US |
| dc.subject | Biset functor | en_US |
| dc.subject | Composition factors | en_US |
| dc.subject | Filtration | en_US |
| dc.subject | Inflation functor | en_US |
| dc.subject | Modular representation algebra | en_US |
| dc.subject | Multiplicity | en_US |
| dc.title | A filtration of the modular representation functor | en_US |
| dc.type | Article | en_US |
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