Continued fraction expansions and permutative representations of the Cuntz algebra ${\mathcal{O}}_{\infty }$

Katsunori Kawamura, Yoshiki Hayashi, Dan Lascu

We show a correspondence between simple continued fraction expansions of irrational numbers and irreducible permutative representations of the Cuntz algebra ${\mathcal{O}}_{\infty }$. Wi…