Browsing by Subject "Primary: 20C20"

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    A general approach to green functors using bisets
    (Taylor & Francis, 2016) Barker, L.
    We introduce a biset-theoretic notion of a Green functor which accommodates the functorial and ring-theoretic structural features of the modular character functor. For any Green functor A in that sense, we introduce an algebra ΛA. Any ΛA-module has the same kind of functorial structure as A and is also a module for the algebra ⊕G A(G) , where G runs over the underlying family of finite groups. In a globally defined scenario and also in a scenario localized to the subquotients of a fixed finite group, we take A to be the modular character functor, and we classify the simple ΛA-modules. © 2016, Copyright © Taylor & Francis Group, LLC.
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    Simple functors of admissible linear categories
    (Springer, 2016) Barker, L.; Demirel, M.
    Generalizing an idea used by Bouc, Thévenaz, Webb and others, we introduce the notion of an admissible R-linear category for a commutative unital ring R. Given an R-linear category (Formula presented.) , we define an (Formula presented.) -functor to be a functor from (Formula presented.) to the category of R-modules. In the case where (Formula presented.) is admissible, we establish a bijective correspondence between the isomorphism classes of simple functors and the equivalence classes of pairs (G, V) where G is an object and V is a module of a certain quotient of the endomorphism algebra of G. Here, two pairs (F, U) and (G, V) are equivalent provided there exists an isomorphism F ← G effecting transport to U from V. We apply this to the category of finite abelian p-groups and to a class of subcategories of the biset category. © 2015, Springer Science+Business Media Dordrecht.