Orientation of quantum Cayley trees and applications

Abstract

We introduce the quantum Cayley graphs associated to quantum discrete groups and study them in the case of trees. We focus in particular on the notion of quantum ascending orientation and describe the associated space of edges at infinity, which is an outcome of the non-involutivity of the edge-reversing operator and vanishes in the classical case. We end with applications to Property AO and K-theory.

41 pages ; late posting of an old article

References in corpus (2)

• K-amenability for amalgamated free products of amenable discrete quantum groups
• Solid von Neumann Algebras

Cited by in corpus (5)

• The Property of Rapid Decay for Discrete Quantum Groups
• Free wreath product quantum groups : the monoidal category, approximation properties and free probability
• $L_p$-Representations of Discrete Quantum Groups
• Growth estimates for discrete quantum groups
• Quantum permutation groups: a survey