Simple section biset functors
| dc.contributor | Ph.D. Program in Mathematics. | |
| dc.contributor.advisor | Coşkun, Olcay. | |
| dc.contributor.author | Muslumov, Ruslan. | |
| dc.date.accessioned | 2023-10-15T11:16:11Z | |
| dc.date.available | 2023-10-15T11:16:11Z | |
| dc.date.issued | 2022 | |
| dc.description.abstract | 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. | |
| dc.format.pages | viii, 60 leaves | |
| dc.identifier.other | MATH 2022 M87 PhD | |
| dc.identifier.uri | https://digitalarchive.library.bogazici.edu.tr/handle/123456789/19904 | |
| dc.publisher | Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022. | |
| dc.subject.lcsh | Simplexes (Mathematics) | |
| dc.title | Simple section biset functors |
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