Stable unital basis, hyperfocal subalgebras and basic Morita equivalences
Group Theory
2022-12-13 v1 Representation Theory
Abstract
We investigate Conjecture 1.6 introduced by Barker and Gelvin in [3], which says that any source algebra of a p-block (p is a prime) of finite group has the unit group containing a basis stabilized by left and right action of the defect group. We will reduce this conjecture to a similar statement about basis of the hyperfocal subalgebras in the source algebra. We will also show that such unital basis of source algebras of two p-blocks, stabilized by left and right action of the defect group, are transported trough basic Morita equivalences.
Keywords
Cite
@article{arxiv.2212.05496,
title = {Stable unital basis, hyperfocal subalgebras and basic Morita equivalences},
author = {Tiberiu Coconet and Constantin-Cosmin Todea},
journal= {arXiv preprint arXiv:2212.05496},
year = {2022}
}