Finite-dimensional algebras not arising as blocks of group algebras

Dave Benson; Benjamin Sambale

doi:10.1515/forum-2023-0037

Finite-dimensional algebras not arising as blocks of group algebras

Dave Benson
, Benjamin Sambale^*

^*Corresponding author for this work

Institute of Algebra, Number Theory and Discrete Mathematics

University of Aberdeen

Research output: Contribution to journal › Article › Research › peer review

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.

Original language	English
Journal	Forum mathematicum
Volume	36
Issue number	2
E-pub ahead of print	1 Jun 2023
DOIs	https://doi.org/10.1515/forum-2023-0037
Publication status	Published - 1 Mar 2024

Keywords

Auslander-Reiten theory
basic algebra
Block theory
Cartan matrix

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1515/forum-2023-0037

Cite this

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title = "Finite-dimensional algebras not arising as blocks of group algebras",

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.",

keywords = "Auslander-Reiten theory, basic algebra, Block theory, Cartan matrix",

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KW - Auslander-Reiten theory

KW - basic algebra

KW - Block theory

KW - Cartan matrix

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DO - 10.1515/forum-2023-0037

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Finite-dimensional algebras not arising as blocks of group algebras

Abstract

Keywords

ASJC Scopus subject areas

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