The boundary of universal discrete quantum groups, exactness, and factoriality
Stefaan Vaes and Roland Vergnioux
Source: Duke Math. J. Volume 140, Number 1
(2007), 35-84.
Abstract
We study the $C^*$-algebras and von Neumann algebras associated with the universal discrete quantum groups. They give rise to full prime factors and simple exact $C^*$-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
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1190730774
Digital Object Identifier: doi:10.1215/S0012-7094-07-14012-2
Mathematical Reviews number (MathSciNet): MR2355067
Zentralblatt MATH identifier: 1129.46062
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