Geodesic
Slow Continued Fractions and Permutative Representations of ${\mathcal{O}}_{N}$
Canadian mathematical bulletin, Tome 63 (2020) no. 4, pp. 787-801

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DOI

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 ${\mathcal{O}}_{2}$.
DOI : 10.4153/S0008439519000821
Mots-clés : Cuntz algebra, continued fractions, permutatative representation, projective linear group, Möbius transformation 
Linden, Christopher. Slow Continued Fractions and Permutative Representations of ${\mathcal{O}}_{N}$. Canadian mathematical bulletin, Tome 63 (2020) no. 4, pp. 787-801. doi: 10.4153/S0008439519000821
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     title = {Slow {Continued} {Fractions} and {Permutative} {Representations} of ${\mathcal{O}}_{N}$},
     journal = {Canadian mathematical bulletin},
     pages = {787--801},
     year = {2020},
     volume = {63},
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     doi = {10.4153/S0008439519000821},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000821/}
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