Open Access
2009 Skew-Product for Group-Valued Edge Labellings of Brateli Diagrams
A. El Kacimi, R. Parthasarathy
Publ. Mat. 53(2): 329-354 (2009).


We associate a Cantor dynamical system to a non-properly ordered Bratteli diagram. 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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A. El Kacimi. R. Parthasarathy. "Skew-Product for Group-Valued Edge Labellings of Brateli Diagrams." Publ. Mat. 53 (2) 329 - 354, 2009.


Published: 2009
First available in Project Euclid: 20 July 2009

zbMATH: 1231.37008
MathSciNet: MR2543855

Primary: 37B10 , 54H20‎

Keywords: Bratteli diagram , Cantor minimal system , substitutional system

Rights: Copyright © 2009 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.53 • No. 2 • 2009
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