A filtration of the modular representation functor


Yaraneri E.

JOURNAL OF ALGEBRA, vol.318, no.1, pp.140-179, 2007 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 318 Issue: 1
  • Publication Date: 2007
  • Doi Number: 10.1016/j.jalgebra.2007.06.030
  • Title of Journal : JOURNAL OF ALGEBRA
  • Page Numbers: pp.140-179

Abstract

Let F and K be algebraically closed fields of characteristics p > 0 and 0, respectively. For any finite group G we denote by KRF(G) = K circle times(Z) G(0) (FG) the modular representation algebra of G over K where G(0)(FG) is the Grothendieck group of finitely generated FG-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 KRF an inflation functor. We show that the composition factors of KRF are precisely the simple inflation functors S-C,V(i) where C ranges over all nonisomorphic cyclic p'-groups and V ranges over all nonisomorphic simple KOut(C)-modules. Moreover each composition factor has multiplicity 1. We also give a filtration of KRF. (c) 2007 Elsevier Inc. All rights reserved.