Slow continued fractions and permutative representations of $\mathcal{O}_N$
Operator Algebras
2019-09-17 v2 Dynamical Systems
Number Theory
Abstract
Representations of the Cuntz algebra 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 --dynamical system ofthe `flip-flop' automorphism of .
Keywords
Cite
@article{arxiv.1810.05948,
title = {Slow continued fractions and permutative representations of $\mathcal{O}_N$},
author = {Christopher Linden},
journal= {arXiv preprint arXiv:1810.05948},
year = {2019}
}