Ergodic Actions of Universal Quantum Groups on Operator Algebras
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We construct ergodic actions of compact quantum groups on C *-algebras and von Neumann algebras, and exhibit phenomena of such actions that are of different nature from ergodic actions of compact groups.
In particular, we construct: (1) an ergodic action of the compact quantum A u (Q) on the type IIIλ Powers factor R λ for an appropriate positive Q∈GL(2, ℝ); (2) an ergodic action of the compact quantum group A u (n) on the hyperfinite II1 factor R; (3) an ergodic action of the compact quantum group A u (Q) on the Cuntz algebra \(\) for each positive matrix Q∈GL(n, ℂ); (4) ergodic actions of compact quantum groups on their homogeneous spaces, as well as an example of a non-homogeneous classical space that admits an ergodic action of a compact quantum group.
KeywordsQuantum Group Compact Group Operator Algebra Universal Quantum Compact Quantum Group
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