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

El Kacimi, A. ; Parthasarathy, R. (2009) Skew-product for group-valued edge labellings of Bratteli diagrams Publicacions Matematiques, 53 (2). pp. 329-354. ISSN 0214-1493

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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.

Item Type:Article
Source:Copyright of this article belongs to Departament de Matematiques, Universitat Autònoma de Barcelona.
Keywords:Cantor Minimal System; Bratteli Diagram; Substitutional System
ID Code:72103
Deposited On:28 Nov 2011 06:00
Last Modified:28 Nov 2011 06:00

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