The boundary of universal discrete quantum groups, exactness and factoriality

Stefaan Vaes (1, 2) , Roland Vergnioux (3, 4)

1 IMJ - Institut de Mathématiques de Jussieu
2 Département de mathématique [Louvain]
3 LMNO - Laboratoire de Mathématiques Nicolas Oresme
4 Institut de Mathématiques, Münster

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.

Domaines: Algèbres d'opérateurs [math.OA]; Algèbres quantiques [math.QA]

Stefaan Vaes, Roland Vergnioux. The boundary of universal discrete quantum groups, exactness and factoriality. Duke Mathematical Journal, 2007, 140, pp.35-84. ⟨hal-00425388⟩