A noncommutative Gauss map | Zendy

Caleb Eckhardt | Zendy

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A noncommutative Gauss map

Author(s) -

Caleb Eckhardt

Publication year - 2011

Publication title -

mathematica scandinavica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.553

H-Index - 30

eISSN - 1903-1807

pISSN - 0025-5521

DOI - 10.7146/math.scand.a-15169

Subject(s) - noncommutative geometry , mathematics , gauss map , extension (predicate logic) , gauss , action (physics) , center (category theory) , bernoulli's principle , algebra over a field , pure mathematics , combinatorics , computer science , physics , chemistry , quantum mechanics , crystallography , programming language , thermodynamics

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 $\mathfrak{A}$ considered separately by F. Boca and D. Mundici. The center of $\ga$ 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 $\mathfrak{A}$ and show that the extension inherits many desirable properties.

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