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      Mackey group categories and their simple functors

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      Author(s)
      Yaylıoğlu, Volkan Dağhan
      Advisor
      Barker, Laurence J.
      Date
      2012
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
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      Abstract
      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.
      Keywords
      Mackey group category
      Puig category
      Brauer category
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      http://hdl.handle.net/11693/15709
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      • Dept. of Mathematics - Master's degree 125
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