Browsing by Author "Muslumov, Ruslan."

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    Green biset functors and representation rings
    (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2017., 2017.) Muslumov, Ruslan.; Coşkun, Olcay.
    In this thesis, we investigate Green biset functors and clasi cation of sipmle modules over a Green biset functors in some special cases. Our aim is to see what conditions on the Green functor makes simple modules over it classi able. We also study the relations between classi cation of simple modules over Green biset functors and classi cation of simple modules over Biset functors .
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    Simple section biset functors
    (Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022., 2022) Muslumov, Ruslan.; Coşkun, Olcay.
    Let G and H be finite groups and k be a commutative unitary ring. The Burnside group B(G,H) is the Grothendieck group of the category of finite (G,H)-bisets. The biset category kC of finite groups is the category defined over finite groups, whose morphism sets are given by the kB(G,H) groups. A biset functor defined on kC, with values in k-Mod is a k-linear functor from kC to the category of k-Mod. The remarkable results as the evaluation of the Dade group of endopermutation modules of a p- group and finding the unit group of the Burnside ring of a p- group are done using the theory of biset functors. Looking for ring objects in the category of biset functors one gets a more sophisticated structure, which is called a Green Biset Functor. Serge Bouc introduced the slice Burnside ring and the section Burnside ring for a finite group G. He also showed that these two rings have a natural structure of a Green Biset Functor. In our work we classify simple modules over the section Burnside ring of G using the approach of the paper Fibered Biset Functors by Robert Boltje and Olcay Coşkun.