Seminario Teoría de Grupos
Cohomological characterisations of groups with low rank representations over a number field
Ponente: Robynn Corveleyn (Université Catholique de Louvain)Fecha: jueves 19 de marzo de 2026 - 10:00Lugar: Aula Naranja, ICMAT
Resumen:
In this talk, I will discuss several aspects of the study of groups through properties of the unit group of their group ring over the ring of integers R of a number field F. In particular, I will cover the “worst-behaved” case: (finite) groups such that all irreducible F-representations are matrix rings of rank at most 2 over a division algebra. Such components are usually excluded in the literature.
I will give characterisations of these groups in terms of cohomological properties of the unit group of the group ring over R. I will also touch on a blockwise variant of the Zassenhaus property, which asks to identify group bases of the group ring. Based on joint work with G. Janssens and D. Temmerman.
