Reduction theorems for a conjecture on basis in source algebras of blocks of finite groups

Fuente: arXiv
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Main Authors: Coconet, Tiberiu, Todea, Constantin-Cosmin
Format: Preprint
Published: 2026
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author Coconet, Tiberiu
Todea, Constantin-Cosmin
author_facet Coconet, Tiberiu
Todea, Constantin-Cosmin
contents The aim of this short research note is to present some results about a conjecture of Barker and Gelvin claiming that any source algebra of a block of a finite group has the unit group containing a basis stabilised by the left and right actions of the defect group. We obtain some reduction theorems for the existence of stable unital basis in source algebras of block algebras. Along the way we investigate this problem for the blocks of some finite simple groups.
format Preprint
id arxiv_https___arxiv_org_abs_2601_21834
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Reduction theorems for a conjecture on basis in source algebras of blocks of finite groups
Coconet, Tiberiu
Todea, Constantin-Cosmin
Representation Theory
Group Theory
The aim of this short research note is to present some results about a conjecture of Barker and Gelvin claiming that any source algebra of a block of a finite group has the unit group containing a basis stabilised by the left and right actions of the defect group. We obtain some reduction theorems for the existence of stable unital basis in source algebras of block algebras. Along the way we investigate this problem for the blocks of some finite simple groups.
title Reduction theorems for a conjecture on basis in source algebras of blocks of finite groups
topic Representation Theory
Group Theory
url https://arxiv.org/abs/2601.21834