Skew-product for group-valued edge labellings of Bratteli diagrams

Abstract

We associate a Cantor dynamical system to a non-properly ordered Bratteli diagram. Group valued edge labelling λ of a Bratteli diagram B give rise to a skew-product Bratelli diagram B(λ) on which the group acts.The quotient by the group action of the associated dynamics can be a nontrivial extension of the dynamics of B. We exhibit a Bratteli diagram for this quotient and construct a morphism to B with unique path lifting property. This is shown to be an isomorphism for the dynamics if a property "loops lifting to loops" is satisfied by B(λ)→B.