English

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 ON\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 CC^*--dynamical system ofthe `flip-flop' automorphism of O2\mathcal{O}_2.

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}
}