Abstract
We investigate Conjecture 1.5 introduced by Barker and Gelvin (J. Gr. Theory 25, 973–995 2022), which says that any source algebra of a p-block (p is a prime) of a finite group has the unit group containing a basis stabilized by the left and right actions of the defect group. We will reduce this conjecture to a similar statement about the bases of the hyperfocal subalgebras in the source algebras. We will also show that such unital bases of source algebras of two p-blocks, stabilized by the left and right actions of the defect group, are transported through basic Morita equivalences.
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We really appreciate the work of an unknown referee for his/her suggestions which significantly improved an older version of this article
Funding
This work was supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS/CCCDI-UEFISCDI, project number PN-III-P1-1.1-TE-2019-0136, within PNCDI III
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The authors T.C. and C.-C. T. contributed equally to this work
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Presented by: Andrew Mathas.
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Coconeţ, T., Todea, CC. Stable Unital Bases, Hyperfocal Subalgebras and Basic Morita Equivalences. Algebr Represent Theor 27, 203–218 (2024). https://doi.org/10.1007/s10468-023-10216-y
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DOI: https://doi.org/10.1007/s10468-023-10216-y