Browsing by Subject "Modular representation algebra"

Filter results by typing the first few letters
Now showing 1 - 1 of 1
  • Thumbnail Image
    ItemOpen Access
    A filtration of the modular representation functor
    (Academic Press, 2007) Yaraneri, E.
    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.