Deformations of some biset-theoretic categories
Author(s)
Advisor
Barker, Laurence JohnDate
2020-09Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
We define the subgroup category, a category on the class of finite groups where the
morphisms are given by the subgroups of the direct products and the composition
is the star product. We also introduce some of its deformations and provide a
criteria for their semisimplicity. We show that biset category can be realized
as an invariant subcategory of the subgroup category, where the composition is
much simpler. With this correspondence, we obtain some of the deformations
of the biset category. We further our methods to the fibred biset category by
introducing the subcharacter partial category. Similarly, we also realize the fibred
biset category and some of its deformations in a category where the composition
is more easily described.
Keywords
Biset functorFibred biset functor
Subgroup category
Partial category
Semisimplicity
Semisimple deformation