Ergodic Actions of Universal Quantum Groups on Operator Algebras |
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Authors: | Shuzhou Wang |
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Institution: | Department of Mathematics, University of California, Berkeley, CA 94720, USA.?E-mail: szwang@math.berkeley.edu, US
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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 Au(Q) on the type IIIu Powers factor Ru for an appropriate positive Q ] GL(2, Â); (2) an ergodic action of the compact quantum group Au(n) on the hyperfinite II1 factor R; (3) an ergodic action of the compact quantum group Au(Q) on the Cuntz algebra _boxclose_boxclose{\cal O}_n for each positive matrix Q ] GL(n, ³); (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. |
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