Idempotent states on quantum groups

Adam Skalski (Lancaster)

Tuesday 31st March, 2009 16:00-17:00 416


Classical Kawada-Ito Theorem says that all idempotent probability measures on locally compact groups are Haar measures on compact subgroups. Since 1995 it has been known that this fails in the case of quantum groups. In this talk we will discuss what all this means, show that all idempotent states on finite quantum groups arise as Haar states on sub quantum `hypergroups' and also present examples of deformations of classical compact Lie groups where all idempotent states come from genuine quantum subgroups (based on the joint work with Uwe Franz and Reiji Tomatsu).

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