Banach Journal of Mathematical Analysis

Baumslag-Solitar group C*-algebras from interval maps

C. Correia Ramos, R. El Harti, Nuno Martins, and Paulo R. Pinto

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Abstract

We yield operators $U$ and $V$ on Hilbert spaces that are parameterized by the orbits of certain interval maps that exhibit chaotic behavior and obey the (deformed) Baumslag--Solitar relation $$UV=e^{2\pi i \alpha} VU^n,\qquad \alpha\in \mathbb{R},\ n\in\mathbb{N}.$$ We then prove that the scalar $e^{2\pi i \alpha}$ can be removed whilst retaining the isomorphism class of the $C^*$-algebra generated by $U$ and $V$. Finally, we simultaneously unitarize $U$ and $V$ by gluing pairs of orbits of the underlying noninvertible dynamical system and investigate these unitary representations under distinct pairs of orbits.

Article information

Source
Banach J. Math. Anal., Volume 8, Number 1 (2014), 138-147.

Dates
First available in Project Euclid: 14 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1381782093

Digital Object Identifier
doi:10.15352/bjma/1381782093

Mathematical Reviews number (MathSciNet)
MR3161688

Zentralblatt MATH identifier
1296.46056

Subjects
Primary: 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]
Secondary: 46L05: General theory of $C^*$-algebras 37B10: Symbolic dynamics [See also 37Cxx, 37Dxx] 37A20: Orbit equivalence, cocycles, ergodic equivalence relations

Keywords
group $C^*$-algebras representations of $C^*$-algebras symbolic dynamics interval maps

Citation

Correia Ramos, C.; El Harti, R.; Martins, Nuno; Pinto, Paulo R. Baumslag-Solitar group C*-algebras from interval maps. Banach J. Math. Anal. 8 (2014), no. 1, 138--147. doi:10.15352/bjma/1381782093. https://projecteuclid.org/euclid.bjma/1381782093


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Banach Journal of Mathematical Analysis

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