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Communications in Mathematical Physics

, Volume 203, Issue 2, pp 481–498 | Cite as

Ergodic Actions of Universal Quantum Groups on Operator Algebras

  • Shuzhou Wang

Abstract:

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 QGL(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 QGL(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.

Keywords

Quantum Group Compact Group Operator Algebra Universal Quantum Compact Quantum Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Shuzhou Wang
    • 1
  1. 1.Department of Mathematics, University of California, Berkeley, CA 94720, USA.¶E-mail: szwang@math.berkeley.eduUS

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