Finite dimensional algebras not arising as blocks of group algebras

TL;DR

This paper introduces new methods for classifying basic algebras of blocks in finite group theory, successfully extending previous classifications and fully classifying blocks with 16-dimensional basic algebras.

Contribution

The paper develops novel techniques for classifying block basic algebras and completes the classification for 16-dimensional cases, advancing the understanding of modular representation theory.

Findings

New classification techniques for block basic algebras

Complete classification of 16-dimensional basic algebras

Extended previous classifications by Linckelmann, Murphy, and Sambale

Abstract

We develop new techniques to classify basic algebras of blocks of finite groups over algebraically closed fields of prime characteristic. We apply these techniques to simplify and extend previous classifications by Linckelmann, Murphy and Sambale. In particular, we fully classify blocks with 16-dimensional basic algebra.