Monograph of the New York Journal of Mathematics
This work was published in the monograph series
New York Journal of Mathematics.
One-sided shift spaces over infinite alphabets
by William Ott, Mark Tomforde, and Paulette N. Willis
We define a notion of (one-sided) shift spaces over infinite alphabets.
Unlike many previous approaches to shift spaces over countable alphabets,
our shift spaces are compact Hausdorff spaces. We examine shift morphisms
between these shift spaces, and identify three distinct classes that generalize
the shifts of finite type. We show that when our shift spaces satisfy a property
that we call "row-finite", shift morphisms on them may be identified with sliding
block codes. As applications, we show that if two (possibly infinite) directed
graphs have edge shifts that are conjugate, then the groupoids of the graphs are
isomorphic, and the C*-algebras of the graphs are isomorphic.
This work was partially supported by a grant from the Simons Foundation
(#210035 to Mark Tomforde) and also partially supported by NSF Mathematical
Sciences Postdoctoral Fellowship DMS-1004675.