Browsing by Subject "Inflation functor"

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    Alcahestic subalgebras of the alchemic algebra and a correspondence of simple modules
    (Elsevier Inc., 2008) Coşkun, Olcay
    The unified treatment of the five module-theoretic notions, transfer, inflation, transport of structure by an isomorphism, deflation and restriction, is given by the theory of biset functors, introduced by Bouc. In this paper, we construct the algebra realizing biset functors as representations. The algebra has a presentation similar to the well-known Mackey algebra. We adopt some natural constructions from the theory of Mackey functors and give two new constructions of simple biset functors. We also obtain a criterion for semisimplicity in terms of the biset functor version of the mark homomorphism. The criterion has an elementary generalization to arbitrary finite-dimensional algebras over a field.
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    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.