Browsing by Subject "Puig category"

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    Mackey group categories and their simple functors
    (2012) Yaylıoğlu, Volkan Dağhan
    Constructing the Mackey group category M using axioms which are reminiscent of fusion systems, the simple RM-functors (the simple functors from the R-linear extension of M to R-modules, where R is a commutative ring) can be classified via pairs consisting of the objects of the Mackey group category (which are finite groups) and simple modules of specific group algebras. The key ingredient to this classification is a bijection between some RM-functors (not necessarily simple) and some morphisms of EndRM(G). It is also possible to define the Mackey group category by using Brauer pairs, or even pointed groups as objects so that this classification will still be valid.
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    The pointed p-groups on a block algebra
    (Elsevier Ltd., 2024-12) Barker, Laurence
    A pointed p-group is a pointed group P gamma such that Pis a p-group. We parameterize the pointed p-groups on a group algebra or on a block algebra of a group algebra. This is equivalent to a parameterization of the isomorphism classes of indecomposable direct summands of the algebra as a bimodule with the group acting on the left and a p-subgroup acting on the right. The parameterization involves p-subgroups and irreducible characters of centralizers of p-subgroups.