The Property of Rapid Decay for Discrete Quantum Groups

TL;DR

This paper extends the classical Property of Rapid Decay to discrete quantum groups, explores examples including free quantum groups, and demonstrates its implications for K-theory of quantum group C*-algebras.

Contribution

It introduces the Property of Rapid Decay for discrete quantum groups, providing equivalent characterizations and applying it to unimodular free quantum groups and K-theory.

Findings

Property of Rapid Decay holds for unimodular free quantum groups

Applications to K-theory of reduced group C*-algebras extend to quantum groups

Equivalent characterizations generalize classical properties

Abstract

We introduce the Property of Rapid Decay for discrete quantum groups by equivalent characterizations that generalize the classical ones. We then 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.