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

Abstract

We define a semidirect product groupoid of a system of partially defined local homeomorphisms $T=(T_1,...,T_r)$. 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 $C^{\ast }(\Lambda )$ and $C^{\ast }({\Lambda }^{op})$.

Cited by in corpus (1)

• Graphs of $C^{\ast }$-correspondences and Fell bundles