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

A. El Kacimi·R. Parthasarathy
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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 $B(λ)\to B$.

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A. El Kacimi, R. Parthasarathy. 2006-02-01. Skew-product for group-valued edge labellings of Bratteli diagrams. https://arxiv.org/abs/math/0506304

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