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Continued Fraction Expansions and Permutative Representations of the Cuntz Algebra O_∞

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: KAWAMURA K., HAYASHI Y., LASCU D.

Editorial: Journal of Number Theory, 129 (12), p.3069 – 308, 2009.

Rezumat:

We show a correspondence between simple continued fraction expansions of irrational numbers and irreducible permutative representations of the Cuntz algebra O_∞. In regard 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 O_∞ with a cycle.

Cuvinte cheie: Cuntz algebra; Permutative representation; Continued fraction expansion

URL: http://dx.doi.org/10.1016/j.jnt.2009.06.003