Abstract
We study the -algebras and von Neumann algebras associated with the universal discrete quantum groups. They give rise to full prime factors and simple exact -algebras. The main tool in our work is the study of an amenable boundary action, yielding the Akemann-Ostrand property. Finally, this boundary can be identified with the Martin or the Poisson boundary of a quantum random walk
Citation
Stefaan Vaes. Roland Vergnioux. "The boundary of universal discrete quantum groups, exactness, and factoriality." Duke Math. J. 140 (1) 35 - 84, 1 October 2007. https://doi.org/10.1215/S0012-7094-07-14012-2
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