A groupoid approach to $C^*$-algebras associated with $\lambda$-graph systems and continuous orbit equivalence of subshifts

Abstract

A $\lambda$-graph system $\frak L$ is a labeled Bratteli diagram with shift operation. It is a generalized notion of finite labeled graph and presents a subshifts. We will study continuous orbit equivalence of one-sided subshifts and topological conjugacy of two-sided subshifts from the view points of groupoids and $C^*$-algebras constructed from $\lambda$-graph systems.