"Saturated Fusion Systems and Idempotents in the Double Burniside Ring"
Abstract: Saturated fusion systems were introduced by Puig as a generalization of the $p$-local structure of a finite group or of a block algebra of a finite group. Broto, Levi and Oliver introduced the notion of characteristic biset associated to a saturated fusion system. This biset is not unique but Ragnarsson proved that there is a unique characteristic idempotent in the p-completed double Burnside ring associated to a saturated fusion system. In this talk, based o a joint work with Kari Ragnarsson, I will give a characterization of saturated fusion systems on a $p$-group $S$ in terms of idempotents in the $p$-local double Burnside ring of $S$ that satisfy a Frobenius reciprocity relation. This helps us to reformulate fusion-theoretic phenomena in the language of idempotents and give some applications in stable homotopy.
Date: Wednesday, May 29, 2013
Place: Mathematics Seminar Room, SA-141
All are most cordially invited.
Tea and cookies will be served after the talk.