Conjectural invariance with respect to the fusion system of an almost-source algebra

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buir.contributor.authorBarker, Laurence
buir.contributor.authorGelvin, Matthew
buir.contributor.orcidBarker, Laurence|0000-0003-3803-9261
buir.contributor.orcidGelvin, Matthew|0000-0001-6529-4116
dc.citation.epage995en_US
dc.citation.issueNumber5en_US
dc.citation.spage973en_US
dc.citation.volumeNumber25en_US
dc.contributor.authorBarker, Laurence
dc.contributor.authorGelvin, Matthew
dc.date.accessioned2023-02-27T06:54:51Z
dc.date.available2023-02-27T06:54:51Z
dc.date.issued2022-03-23
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractWe show that, given an almost-source algebra 𝐴 of a 𝑝-block of a finite group 𝐺, then the unit group of 𝐴 contains a basis stabilized by the left and right multiplicative action of the defect group if and only if, in a sense to be made precise, certain relative multiplicities of local pointed groups are invariant with respect to the fusion system. We also show that, when 𝐺 is 𝑝-solvable, those two equivalent conditions hold for some almost-source algebra of the given 𝑝-block. One motive lies in the fact that, by a theorem of Linckelmann, if the two equivalent conditions hold for 𝐴, then any stable basis for 𝐴 is semicharacteristic for the fusion system.en_US
dc.identifier.doi10.1515/jgth-2020-0205en_US
dc.identifier.eissn1435-4446
dc.identifier.urihttp://hdl.handle.net/11693/111789
dc.language.isoEnglishen_US
dc.publisherWalter de Gruyter GmbHen_US
dc.relation.isversionofhttps://doi.org/10.1515/jgth-2020-0205en_US
dc.source.titleJournal of Group Theoryen_US
dc.titleConjectural invariance with respect to the fusion system of an almost-source algebraen_US
dc.typeArticleen_US
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