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Slow Continued Fractions and Permutative Representations of ${\mathcal{O}}_{N}$

Published online by Cambridge University Press:  03 January 2020

Christopher Linden*
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, USA Email: [email protected]

Abstract

Representations of the Cuntz algebra ${\mathcal{O}}_{N}$ are constructed from interval dynamical systems associated with slow continued fraction algorithms introduced by Giovanni Panti. Their irreducible decomposition formulas are characterized by using the modular group action on real numbers, as a generalization of results by Kawamura, Hayashi, and Lascu. Furthermore, a certain symmetry of such an interval dynamical system is interpreted as a covariant representation of the $C^{\ast }$-dynamical system of the “flip-flop” automorphism of ${\mathcal{O}}_{2}$.

Type
Article
Copyright
© Canadian Mathematical Society 2020

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