"Saturated
Fusion Systems and Idempotents in the Double Burniside Ring"
By
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
Time: 14.00-15.00
Place: Mathematics Seminar Room,
SA-141
All are most cordially invited.
Tea and cookies will be served after the talk.