Embedding ergodic actions of compact quantum groups on C*-algebras into quotient spaces

Abstract

The notion of compact quantum subgroup is revisited and an alternative definition is given. Induced representations are considered and a Frobenius reciprocity theorem is obtained. A relationship between ergodic actions of compact quantum groups on C*-algebras and topological transitivity is investigated. A sufficient condition for embedding such actions in quantum quotient spaces is obtained.

31 pages, Latex; The assumptions of Prop. 2.5 of the published version are strengthened, leading to the equivalence between closed coideals and Wang's notion of Woronowicz C*-ideal for nuclear C*algebras and leaving the equivalence problem open in the general case

References in corpus (1)

• Symmetries of quantum spaces. Subgroups and quotient spaces of quantum $SU(2)$ and $SO(3)$ groups