Multiply generated dynamical systems and the duality of higher rank graph algebras

2008/11/11 by Popescu, Ionel, Popescu, Iulian
#17O13 #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.0811.1654

Abstract

We define a semidirect product groupoid of a system of partially defined local homeomorphisms T=(T₁,..., T_r). We prove that this construction gives rise to amenable groupoids. The associated algebra is a Cuntz-like algebra. We use this construction for higher rank graph algebras in order to give a topological interpretation for the duality in E-theory between C^*(Λ) and C^*(Λ^op).

Related

• Groupoid models for the C*-algebras of topological higher-rank graphs
• Topological graphs and singly generated dynamical systems
• Product systems of graphs and the Toeplitz algebras of higher-rank graphs
• Partial transformation groupoids attached to graphs and semigroups
• Categorising the operator algebras of groupoids and higher-rank graphs