Ultragraphs and shifts spaces over infinite alphabets
Dynamical Systems
2015-10-19 v2 Operator Algebras
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.
Keywords
Cite
@article{arxiv.1510.04649,
title = {Ultragraphs and shifts spaces over infinite alphabets},
author = {Daniel Gonçalves and Danilo Royer},
journal= {arXiv preprint arXiv:1510.04649},
year = {2015}
}