Finite dimensional algebras not arising as blocks of group algebras

2023/01/25 by Dave Benson, Benjamin Sambale, Benson, Dave +1
Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2301.10537

openalex publication_date 2023/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• A 9-dimensional algebra which is not a block of a finite group
• Blocks of group algebras are derived simple
• Classification of finite dimensional simple Lie algebras in prime characteristics
• Algebras of finite global dimension
• Isotypic blocks are functorially equivalent