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2014 Baumslag-Solitar group C*-algebras from interval maps
C. Correia Ramos, R. El Harti, Nuno Martins, Paulo R. Pinto
Banach J. Math. Anal. 8(1): 138-147 (2014). DOI: 10.15352/bjma/1381782093

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.

Citation

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C. Correia Ramos. R. El Harti. Nuno Martins. Paulo R. Pinto. "Baumslag-Solitar group C*-algebras from interval maps." Banach J. Math. Anal. 8 (1) 138 - 147, 2014. https://doi.org/10.15352/bjma/1381782093

Information

Published: 2014
First available in Project Euclid: 14 October 2013

zbMATH: 1296.46056
MathSciNet: MR3161688
Digital Object Identifier: 10.15352/bjma/1381782093

Subjects:
Primary: 46L55
Secondary: 37A20, 37B10, 46L05

Rights: Copyright © 2014 Tusi Mathematical Research Group

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