Group representations: idempotents in group algebras and applications to units (FWOTM613)

The aim of our research is to describe all representations of finite groups, both over the rationals and finite fields, and to use this in order to find units in (integral) group rings. In particular one has to determine first the primitive central idempotent of the associated group algebra and second one has to determine (internally) primitive idempotents and a complete set of elementary matrices. Finally also the centers have to be described. This will be the main focus of the proposed research. We will, as a consequence, be able to tackle some fundamental open problems on group algebras and more generally on Z-orders.

Keywords:Mathematics

Disciplines:Mathematical sciences and statistics