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

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dc.creatorKawamura, Katsunori
dc.creatorHayashi, Yoshiki
dc.creatorLascu, Dan
dc.date2009-01-15
dc.date.accessioned2026-07-07T12:29:38Z
dc.date.available2026-07-07T12:29:38Z
dc.descriptionWe show a correspondence between simple continued fraction expansions of irrational numbers and irreducible permutative representations of the Cuntz algebra ${\cal O}_{\infty}$. With respect to the correspondence, it is shown that the equivalence of real numbers with respect to modular transformations is equivalent to the unitary equivalence of representations. Furthermore, we show that quadratic irrationals are related to irreducible permutative representations of ${\cal O}_{\infty}$ with a cycle.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/0901.2186
dc.identifierhttp://arxiv.org/abs/0901.2186
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/215941
dc.subjectOperator Algebras
dc.subjectNumber Theory
dc.subject11A55; 46K10
dc.titleContinued fraction expansions and permutative representations of the Cuntz algebra ${\cal O}_{\infty}$
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