Idempotent States on Locally Compact Groups and Quantum Groups

Abstract

This is a short survey on idempotent states on locally compact groups and locally compact quantum groups. The central topic is the relationship between idempotent states, subgroups and invariant C*-subalgebras. We concentrate on recent results on locally compact quantum groups, but begin with the classical notion of idempotent probability measure. We also consider the ‘intermediate’ case of idempotent states in the Fourier–Stieltjes algebra: this is the dual case of idempotent probability measures and so an instance of idempotent states on a locally compact quantum group.KeywordsIdempotent stateidempotent probability measurelocally compact quantum groupcompact quantum subgroup.