Resumen de A noncommutative Gauss map

Caleb Eckhardt

• 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.