Duke Mathematical Journal

The boundary of universal discrete quantum groups, exactness, and factoriality

Stefaan Vaes and Roland Vergnioux

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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

Article information

Source
Duke Math. J. Volume 140, Number 1 (2007), 35-84.

Dates
First available in Project Euclid: 25 September 2007

Permanent link to this document
https://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

Subjects
Primary: 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]
Secondary: 46L65: Quantizations, deformations 46L54: Free probability and free operator algebras

Citation

Vaes, Stefaan; Vergnioux, Roland. The boundary of universal discrete quantum groups, exactness, and factoriality. Duke Math. J. 140 (2007), no. 1, 35--84. doi:10.1215/S0012-7094-07-14012-2. https://projecteuclid.org/euclid.dmj/1190730774.


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