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Ergodic Actions of Universal Quantum Groups on Operator Algebras | | Shuzhou Wang
; | | Date: |
17 Jul 1998 | | Journal: | Commun. Math. Phys. 203 (1999), 481-498 | | Subject: | Operator Algebras; Quantum Algebra | math.OA math.QA | | 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 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. | | Source: | arXiv, math.OA/9807093 | | Services: | Forum | Review | PDF | Favorites | |
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