A Construction of finite index C*-algebra inclusions from free actions of compact quantum groups

Abstract

Given an action of a compact quantum group on a unital C*-algebra, one can consider the associated Wassermann-type C*-algebra inclusions. One amplifies the original action with the adjoint action associated with a finite-dimensional unitary representation, and considers the induced inclusion of fixed point algebras. We show that this inclusion is a finite index inclusion of C*-algebras when the quantum group acts freely. Along the way, two natural definitions of freeness for a compact quantum group action, due respectively to D. Ellwood and M. Rieffel, are shown to be equivalent. © 2013 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.