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dc.contributor.authorBoltje, Robert
dc.contributor.authorDanz, Susanne
dc.date.accessioned2012-07-03T12:00:00Z
dc.date.accessioned2016-10-05T14:14:23Z
dc.date.available2012-07-03T12:00:00Z
dc.date.available2016-10-05T14:14:23Z
dc.date.issued2012-07-03
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1212
dc.descriptionResearch in Pairs 2012en_US
dc.description.abstractFor a finite group $G$, we introduce a multiplication on the $\mathbb{Q}$-vector space with basis $\mathscr{S}_{G\times G}$, the set of subgroups of ${G \times G}$. The resulting $\mathbb{Q}$-algebra $\tilde{A}$ can be considered as a ghost algebra for the double Burnside ring $B(G,G)$ in the sense that the mark homomorphism from $B(G,G)$ to $\tilde{A}$ is a ring homomorphism. Our approach interprets $\mathbb{Q}B(G,G)$ as an algebra $eAe$, where $A$ is a twisted monoid algebra and $e$ is an idempotent in $A$. The monoid underlying the algebra $A$ is again equal to $\mathscr{S}_{G\times G}$ with multiplication given by composition of relations (when a subgroup of $G \times G$ is interpreted as a relation between $G$ and $G$). The algebras $A$ and $\tilde{A}$ are isomorphic via Möbius inversion in the poset $\mathscr{S}_{G\times G}$. As an application we improve results by Bouc on the parametrization of simple modules of $\mathbb{Q}B(G,G)$ and also of simple biset functors, by using results by Linckelmann and Stolorz on the parametrization of simple modules of finite category algebras. Finally, in the case where G is a cyclic group of order n, we give an explicit isomorphism between $\mathbb{Q}B(G,G)$ and a direct product of matrix rings over group algebras of the automorphism groups of cyclic groups of order $k$, where $k$ divides $n$.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2012,09
dc.subjectBurnside ringen_US
dc.subjectDouble Burnside ringen_US
dc.subjectMark homomorphismen_US
dc.subjectGhost ringen_US
dc.subjectSchur functoren_US
dc.subjectBiseten_US
dc.subjectBiset functoren_US
dc.subjectTwisted category algebraen_US
dc.titleGhost Algebras of Double Burnside Algebras via Schur Functorsen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2012-09
local.scientificprogramResearch in Pairs 2012
local.series.idOWP-2012-09
local.subject.msc19
local.subject.msc20
dc.identifier.urnurn:nbn:de:101:1-201207047049
dc.identifier.ppn1651531994


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