Quantum Brauer groups of finite groups (R-9878)

In this proposal, I will describe completely the Brauer group of a finite group using the recent developed braided bi-Galois theory, and investigate the role of this Brauer group in the Brauer-Picard group of the given finite group. In particular, we will compute the Brauer group of symmetric groups in low degrees. The computation of those Brauer-Long groups is strongly related to the representation theory of the quantum doubles of the symmetric groups. Next, I will investigate the Brauer-Picard groups of symmetric groups in low degrees. These groups have strong relations with the aforementioned Brauer groups of finite groups, but they are not contained in one or another. Interesting properties are highly expected.

Keywords:ENVELOPING ALGEBRAS OF LIE ALGEBRAS

Disciplines:Associative rings and algebras, Category theory, homological algebra

Project type:Collaboration project