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arXiv · 2212.05496

Stable unital basis, hyperfocal subalgebras and basic Morita equivalences

Tiberiu Coconet·Constantin-Cosmin Todea
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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.

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BibTeXRIS

Tiberiu Coconet, Constantin-Cosmin Todea. 2022-12-11. Stable unital basis, hyperfocal subalgebras and basic Morita equivalences. https://arxiv.org/abs/2212.05496

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