# A Noncommutative Gauss map - Mathematics > Operator Algebras

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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/