 

William Ott, Mark Tomforde, and Paulette N. Willis
Onesided shift spaces over infinite alphabets view print


Published: 
January 21, 2014 
Keywords: 
Symbolic dynamics, onesided shift spaces, sliding block codes, infinite alphabets, shifts of finite type, C*algebras 
Subject: 
37B10, 46L55 


Abstract
We define a notion of (onesided) 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 "rowfinite", 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.


Acknowledgements
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 DMS1004675.


Author information
William Ott:
Department of Mathematics, University of Houston, Houston, TX 772043008, USA
ott@math.uh.edu
Mark Tomforde:
Department of Mathematics, University of Houston, Houston, TX 772043008, USA
tomforde@math.uh.edu
Paulette N. Willis:
Department of Mathematics, University of Houston, Houston, TX 772043008, USA
pnwillis@math.uh.edu

