Simple functors of admissible linear categories

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dc.citation.epage472en_US
dc.citation.issueNumber2en_US
dc.citation.spage463en_US
dc.citation.volumeNumber19en_US
dc.contributor.authorBarker, L.en_US
dc.contributor.authorDemirel, M.en_US
dc.date.accessioned2018-04-12T10:57:32Z
dc.date.available2018-04-12T10:57:32Z
dc.date.issued2016en_US
dc.departmentDepartment of Mathematicsen_US
dc.departmentDepartment of Economicsen_US
dc.description.abstractGeneralizing an idea used by Bouc, Thévenaz, Webb and others, we introduce the notion of an admissible R-linear category for a commutative unital ring R. Given an R-linear category (Formula presented.) , we define an (Formula presented.) -functor to be a functor from (Formula presented.) to the category of R-modules. In the case where (Formula presented.) is admissible, we establish a bijective correspondence between the isomorphism classes of simple functors and the equivalence classes of pairs (G, V) where G is an object and V is a module of a certain quotient of the endomorphism algebra of G. Here, two pairs (F, U) and (G, V) are equivalent provided there exists an isomorphism F ← G effecting transport to U from V. We apply this to the category of finite abelian p-groups and to a class of subcategories of the biset category. © 2015, Springer Science+Business Media Dordrecht.en_US
dc.identifier.doi10.1007/s10468-015-9583-2en_US
dc.identifier.eissn1572-9079
dc.identifier.issn1386-923X
dc.identifier.urihttp://hdl.handle.net/11693/36926
dc.language.isoEnglishen_US
dc.publisherSpringeren_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s10468-015-9583-2en_US
dc.source.titleAlgebras and Representation Theoryen_US
dc.subjectBiset categoryen_US
dc.subjectGroup categoryen_US
dc.subjectQuiver algebra of a linear categoryen_US
dc.subjectSeeds of simple functorsen_US
dc.subjectEquivalence classesen_US
dc.subjectGroup theoryen_US
dc.subjectSet theoryen_US
dc.subjectBiset categoryen_US
dc.subjectFunctorsen_US
dc.subjectGroup categoryen_US
dc.subjectIsomorphism classen_US
dc.subjectLinear categoriesen_US
dc.subjectp-Groupen_US
dc.subjectAlgebraen_US
dc.subjectPrimary: 20C20en_US
dc.subjectSecondary: 20J99en_US
dc.titleSimple functors of admissible linear categoriesen_US
dc.typeArticleen_US

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