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

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

2005-06-15

arxiv.org/abs/math/0506304v2

Mathematics

Dynamical Systems

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

Scientific paper

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

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