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Abstract: The aim of this paper is to transfer the Gauss map, which is a Bernoullishift for continued fractions, to the noncommutative setting. We feel that anatural place for such a map to act is on the AF algebra $\mathfrak{A}$considered separately by F. Boca and D. Mundici. The center of $\ga$ isisomorphic to $C0,1$, so we first consider the action of the Gauss map on$C0,1$ and then extend the map to $\mathfrak{A}$ and show that the extensioninherits many desirable properties.

Author: Caleb Eckhardt

Source: https://arxiv.org/


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