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.

arXiv comment41 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

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• Quantum graphs, subfactors and tensor categories I
• Strong 1-Boundedness of Unimodular Free Orthogonal Quantum Groups