Browsing by Subject "biset functor"

Now showing 1 - 3 of 3

Open Access
Canonical induction for trivial source rings
(2013) Büyükçolak, Yasemin
We discuss the canonical induction formula for some special Mackey functors by following the construction of Boltje. These functors are the ordinary and modular character rings and the trivial source rings. Making use of a natural correspondence between the Mackey algebra and the finite algebra spanned by the three kinds of basic bisets, namely the conjugation, restriction and induction, we investigate the canonical induction formula in terms of the theory of bisets. We focus on the trivial source rings and the canonical induction formula for them. The main aim is to get an explicit formula for the canonical induction of regular bimodules in the trivial source. This gives a first step towards for the canonical induction of blocks.
Open Access
A correspondence of simple alcahestic group functors
(2008) Coşkun, Olcay
Representation theory of finite groups associates two classical constructions to a group G, namely the representation ring of G and the Burnside ring of G. These rings share a special structure that comes from three classical maps, namely restriction, conjugation, and transfer maps. These are not the only objects having this structure and the theory of Mackey functors, introduced by Green, unifies the treatment of such objects. The above constructions share a further structure that comes from two other maps, the inflation map and the deflation map. Unified treatment of the objects having this further structure was introduced by Bouc [4]. These objects are called biset functors. Between Mackey functors and biset functors there lies more natural constructions, for example the functor of group (co)homology. In order to handle these intermediate structures, Bouc introduced another concept, now known as globallydefined Mackey functors, a name given by Webb. In this thesis, we unify the above theories by considering the algebra whose module category is equivalent to the category of biset functors and by introducing alcahestic group functors. Our main results classify and describe simple alcahestic group functors and give a criterion of semisimplicity for the categories of these functors.
Open Access
Simple functors of admissible linear categories
(2013) Demirel, Merve
We review the notion of an admissible R-linear category for a commutative unital ring R and we prove the classification theorem for simple functors of such a category by Barker-Boltje which states that there is a bijective correspondence between the seeds of linear category and simple linear functors. We also review the application of this theorem by Bouc to the biset category by showing that the biset category is admissible. Finally, we classify the simple functors for the category of finite abelian p-groups and show that, for a natural number n, the n-th simple functor is non-zero on precisely the groups which have exponent at least pn .