Hochschild Cohomology of Group Algebras and Blocks

Abstract

In this seminar, I will give a basic introduction to Hochschild cohomology, introduced by Hochschild in 1945. It can be viewed as a generalisation of group cohomology to finite-dimensional algebras. For a finite-dimensional k-algebra A, Hochschild cohomology can be defined using a projective bimodule resolution of A, but it also admits concrete interpretations in low degrees. In particular, the first Hochschild cohomology group admits a natural Lie algebra structure. We will then explore how the Hochschild cohomology of group algebras and blocks is related to ordinary group cohomology.

Biography

Jialin Wang received her PhD from Nanyang Technological University in 2024, under the supervision of Kay Jin Lim. She is currently a Research Assistant at City St George’s, University of London, working with Markus Linckelmann. Her research focuses on modular representation theory and the cohomology of blocks and finite group algebras.

AToM@MAS

This talk is part of a new regular seminar series we are organizing called AToM@MAS. This stands for The Algebra, Topology, and Mathematical Physics Seminar. This series is intended to complement the regular MAS Seminar Series by providing speakers with an opportunity to give supplementary introductory talks aimed at a wider mathematical audience, including researchers not working in the discipline in question. It also offers researchers at all career stages within SPMS a platform to present their work and hosts in-depth learning seminars on topics of interest within algebra, topology, mathematical physics, and their interdisciplinary spaces.