一个非交换Gauss映射
A Noncommutative Gauss map
摘要：
本文的目的是将高斯映射，这是一个连分数的伯努利移位，到非交换设置。我们认为，这样一个映射作用的自然位置是F单独考虑的AF代数$\mathfrak{A}$上。Boca和D.蒙迪奇由于$\ga$的中心同构于$C[0,1]$，因此我们首先考虑高斯映射在$C[0,1]$上的作用，然后将其推广到$\mathfrak{A}$，并证明了推广后的映射继承了许多理想的性质.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
