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

Abstract

Group valued edge labellings $λ$ of a Bratteli diagram $B$ give rise to a skew-product Bratteli 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 $B(λ)\to B$.

32 pages, 3 figures; Speculation at the end of previous version settled; some typos fixed