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The boundary of universal discrete quantum groups, exactness and factoriality

Stefaan Vaes·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.

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Stefaan Vaes, Roland Vergnioux. 2006-07-07. The boundary of universal discrete quantum groups, exactness and factoriality. https://arxiv.org/abs/math/0509706

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