Revistes Catalanes amb Accés Obert (RACO)

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

A. El Kacimi, R. Parthasarathy


We associate a Cantor dynamical system to a non-properly ordered Bratteli diagram. 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 con- struct 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.

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