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Disputation Georg Lehner

22.11.2021 | 16:00
Thema der Dissertation:
The passage from the integral to the rational group ring in algebraic K-theory
Thema der Disputation:
Modular Representation Theory and Berman's Theorem
Abstract: Modular representation theory is the study of representations of a finite group $G$ over a base field $k$ with non-zero characteristic $p$. Many results which hold in ordinary representation theory require that the base field is algebraically closed and of characteristic $0$, and are not true in the modular setting. One key statement needed for the study of character tables is that the number of irreducible $G$-representations over an algebraically closed field of character zero is equal to the number of conjugacy classes of $G$. The appropriate generalization is given by Berman's Theorem, which states that the number of irreducible $G$-representations over an arbitrary field $k$ is equal to the number of $k$-conjugacy classes of $p$-regular elements of $G$, where $p$ is the characteristic of $k$. We will give a sketch of a proof of Berman's theorem using Brauer characters and give some applications to the algebraic $K$-theory of the group algebras $\mathbb{F}_p G, \mathbb{Z}_p G$ and $\mathbb{Q}_p G$.

Zeit & Ort

22.11.2021 | 16:00