Mackey group categories and their simple functors
Author(s)
Advisor
Date
2012Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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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.