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

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

2012-01-19

arxiv.org/abs/1201.4022v1

Mathematics

Operator Algebras

24 pages

Scientific paper

Given an action of a compact quantum group on a unital C*-algebra, one can amplify the action with an adjoint representation of the quantum group on a finite dimensional matrix algebra, and consider the resulting inclusion of fixed point algebras. We show that this inclusion is a finite index inclusion of C*-algebras when the quantum group acts freely. We show that two natural definitions for a quantum group to act freely, namely the Ellwood condition and the saturatedness condition, are equivalent.

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