关于与最小位移空间相关的cuntz-pimsner c *-代数的核维

Pub Date : 2021-12-31 DOI:10.4153/S0008414X22000645

Zhuofeng He, Sihan Wei

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引用次数: 1

摘要

对于有限字母表上的每一个单侧移位空间$X$，左特殊元素是在$X$中至少有两个在移位操作下的原像的点。本文证明了当$X$为最小值且$X$的左特殊元素个数有限时，Cuntz-Pimsner $C^*$-代数$\mathcal{O}_X$具有核维数1。这是通过彻底描述$X$的封面来完成的，它也恢复了T. Carlsen和S. Eilers之前发现的精确序列。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A NOTE ON THE NUCLEAR DIMENSION OF CUNTZ-PIMSNER C*-ALGEBRAS ASSOCIATED WITH MINIMAL SHIFT SPACES

For every one-sided shift space $X$ over a finite alphabet, left special elements are those points in $X$ having at least two preimages under the shift operation. In this paper, we show that the Cuntz-Pimsner $C^*$-algebra $\mathcal{O}_X$ has nuclear dimension 1 when $X$ is minimal and the number of left special elements in $X$ is finite. This is done by describing thoroughly the cover of $X$ which also recovers an exact sequence, discovered before by T. Carlsen and S. Eilers.

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