This 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.Dieses 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.Boltje, RobertDanz, Susanne2019-06-2820121864-7596https://doi.org/10.34657/2418https://oa.tib.eu/renate/handle/123456789/1884For a finite group G, we introduce a multiplication on the Q-vector space with basis SG×G, the set of subgroups of G × G. The resulting Q-algebra 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 A˜ is a ring homomorphism. Our approach interprets QB(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 SG×G with multiplication given by composition of relations (when a subgroup of G × G is interpreted as a relation between G and G). The algebras A and A˜ are isomorphic via Mo¨bius inversion in the poset SG×G. As an application we improve results by Bouc on the parametrization of simple modules of QB(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 QB(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.application/pdfeng510Burnside ringdouble Burnside ringmark homomorphismghost ringSchur functorbisetbiset functortwisted category algebraReport