Duke Mathematical Journal

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

Stefaan Vaes and Roland Vergnioux

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

First available in Project Euclid: 25 September 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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