A noncommutative Gauss map

• Autores: Caleb Eckhardt
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 108, Nº 2, 2011, págs. 233-250
• Idioma: inglés
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• Resumen

  • The aim of this paper is to transfer the Gauss map, which is a Bernoulli shift for continued fractions, to the noncommutative setting. We feel that a natural place for such a map to act is on the AF algebra A considered separately by F. Boca and D. Mundici. The center of A is isomorphic to C[0,1], so we first consider the action of the Gauss map on C[0,1] and then extend the map to A and show that the extension inherits many desirable properties.