MVEX01-17-04 Finite hypergroups and their representation theory

The representation theory of finite groups has been developed significantly during last century and many of its applications emerged in different fields of Mathematics.

Roughly speaking, a discrete hypergroup is a set equipped with an extra structure, which leads to the construction of a Banach algebra on the Banach space of all absolutely summable functions on the hypergroup. This Banach algebra is called the hypergroup algebra. The multiplication of two point mass measures is also supposed to be a finitely-supported probability measure and therefore the hypergroup structure has a probabilistic taste, since one may roughly express that the outcome of the action of two elements of a hypergroup is chosen ‘randomly’.

We will start by learning the theory of finite groups and hypergroups simultaneously. We focus on many examples of finite hypergroups specificity in the graph theory and group theory. Then we try to rebuild the character theory of finite hypergroups (having the group case in mind) and try to see how far we can push an analogy.

Projektet är lämpligt GU-studenter med inriktning mot matematik men också för chalmersstudenter med extra intresse för algebra, analys och teoretiska resonemang.

Obs! För GU-studenter räknas projektet som ett projekt i Matematik (MMG900/MMG910).

Projektkod MVEX01-17-04
Gruppstorlek 2-3
Speciella förkunskapskrav Basic knowledge in Linear Algebra and rather a little Graph theory
Handledare Mahmood Alaghmandan, 031-7725374,  mahala@chalmers.se
Examinator Maria Roginskaya, Marina Axelson-Fisk
Insti