The boundary of universal discrete quantum groups, exactness and factoriality

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

2005-09-29

arxiv.org/abs/math/0509706v3

Duke Mathematical Journal, Vol. 140, 2007, p. 35--84.

Mathematics

Operator Algebras

Correction in postal adress

Scientific paper

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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