Ergodic Actions of Universal Quantum Groups on Operator Algebras

Details Ergodic Actions of Universal Quantum Groups on Operator Algebras Ergodic Actions of Universal Quantum Groups on Operator Algebras

1998-07-17

arxiv.org/abs/math/9807093v2

Commun. Math. Phys. 203 (1999), 481-498

Mathematics

Operator Algebras

AMSLATEX, 22 pages, Accepted for publication in Commun. Math. Phys. A few minor changes are made according to the referee's su

Scientific paper

10.1007/s002200050622

We construct ergodic actions of compact quantum groups on C^*-algebras and von Neumann algebras, and exhibit phenomena of such actions that are of a different nature from ergodic actions of compact Lie groups. In particular, we construct: (1). ergodic actions of the compact quantum groups $A_u(Q)$ on the Powers factors; (2). ergodic actions of the compact quantum groups $A_u(n)$ on the hyperfinite II_1 factor; (3). ergodic actions of the compact quantum groups $A_u(Q)$ on the Cuntz algebras; (4). ergodic actions of general compact quantum groups on their homogeneous spaces and an example of a non-homogeneous classical space that nevertheless admits an ergodic action of a compact quantum group.

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