Actions of compact quantum groups on 𝐶*-algebras

Abstract

In this paper we investigate a structure of the fixed point algebra under an action of compact matrix quantum group on a C ∗ C^* -algebra B \mathcal {B} . We also show that the categories of C \mathcal C -comodules in B \mathcal B and inner endomorphisms restricted to the fixed point algebra coincide when the relative commutant of the fixed point algebra is trivial. Next we show a version of the Tannaka duality theorem for twisted unitary groups.