Journal of Operator Theory

Volume 57, Issue 2, Spring 2007 pp. 303-324.

The property of rapid decay for discrete quantum groups

Authors: Roland Vergnioux
Author institution: Laboratoire de Math\'ematiques Nicolas Oresme, Universit\'e de Caen, 14000 Caen, France

Summary: We introduce the Property of Rapid Decay for discrete quantum groups by equivalent characterizations that generalize the classical ones. We investigate examples, proving in particular the Property of Rapid Decay for unimodular free quantum groups. We finally check that the applications to the $K$-theory of the reduced group $C^*$-algebras carry over to the quantum case.

Keywords: Quantum groups, rapid decay, group $C^*$-algebras

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