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arXiv · 2112.15519

A note on the nuclear dimension of Cuntz-Pimsner $C^*$-algebras associated with minimal shift spaces

Zhuofeng He·Sihan Wei
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Abstract

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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Zhuofeng He, Sihan Wei. 2021-12-31. A note on the nuclear dimension of Cuntz-Pimsner $C^*$-algebras associated with minimal shift spaces. https://doi.org/10.4153/s0008414x22000645

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