A Remark on Quantum Group Actions and Nuclearity

Abstract

Let H be a compact quantum group with faithful Haar measure and bounded counit. If H acts on a C*-algebra A, we show that A is nuclear if and only if its fixed-point subalgebra is nuclear. As a consequence H is a nuclear C*-algebra.

12 pages, LateX 2e

References in corpus (1)

• Ergodic Actions of Universal Quantum Groups on Operator Algebras

Cited by in corpus (12)

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• A construction of actions on Kirchberg algebras which induce given actions on their K-groups
• Subproduct systems with quantum group symmetry. II
• Quantum symmetry groups of noncommutative tori
• Amenability, completely bounded projections, dynamical systems and smooth orbits
• Nuclear and type I crossed products of C*-algebras by group and compact quantum group actions
• Growth rates of dimensional invariants of compact quantum groups and a theorem of Hoegh-Krohn, Landstad and Stormer