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arXiv · 1510.04649

Ultragraphs and shifts spaces over infinite alphabets

Daniel Gonçalves·Danilo Royer
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Abstract

In this paper we further develop the theory of one sided shift spaces over infinite alphabets, characterizing one-step shifts as edge shifts of ultragraphs and partially answering a conjecture regarding shifts of finite type (we show that there exists shifts of finite type that are not conjugate, via a conjugacy that is eventually finite periodic, to an edge shift of a graph ). We also show that there exists edge shifts of ultragraphs that are shifts of finite type, but are not conjugate to a full shift, a result that is not true for edge shifts of graphs. One of the key results needed in the proofs of our conclusions is the realization of a class of ultragraph C*-algebras as partial crossed products, a result of interest on its own.

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Daniel Gonçalves, Danilo Royer. 2015-10-16. Ultragraphs and shifts spaces over infinite alphabets. https://arxiv.org/abs/1510.04649

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