3 December 2025 — Padova

On the non-vanishing of the first Hochschild cohomology of blocks of group algebras

Lleonard Rubio y Degrassi, University of Padova

Abstract

Hochschild cohomology is a powerful invariant under various categorical equivalences, such as derived equivalences or stable equivalences of Morita type. However, our understanding of Hochschild cohomology of finite-dimensional algebras remains quite limited. In this talk, I will focus on recent advances on a conjecture posed by Linckelmann, which predicts that if \(B\) is a block of a group algebra \(kG\) with a nontrivial defect group, then the first Hochschild cohomology of \(B\) is nonzero. This is joint work with Benjamin Briggs.