Dynamical Systems and Groupoid Algebras on Higher Rank Graphs

Abstract

For a locally compact higher rank graph Λ, we construct a two-sided path space Λ ∆ with shift homeomorphism σ and its corresponding path groupoid Γ. Then we find equivalent conditions of aperiodicity, cofinality and irreducibility of Λ in (Λ ∆ , σ), Γ, and the groupoid algebra C * (Γ).