Publicacions Matemàtiques

Skew-Product for Group-Valued Edge Labellings of Brateli Diagrams

A. El Kacimi and R. Parthasarathy

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Abstract

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 $B(\lambda )\to B$.

Article information

Source
Publ. Mat., Volume 53, Number 2 (2009), 329-354.

Dates
First available in Project Euclid: 20 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.pm/1248095659

Mathematical Reviews number (MathSciNet)
MR2543855

Zentralblatt MATH identifier
1231.37008

Subjects
Primary: 37B10: Symbolic dynamics [See also 37Cxx, 37Dxx] 54H20: Topological dynamics [See also 28Dxx, 37Bxx]

Keywords
Cantor minimal system Bratteli diagram substitutional system

Citation

El Kacimi, A.; Parthasarathy, R. Skew-Product for Group-Valued Edge Labellings of Brateli Diagrams. Publ. Mat. 53 (2009), no. 2, 329--354. https://projecteuclid.org/euclid.pm/1248095659


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