Conjugacy of subshifts via the associated algebras.

Abstract

In this talk, we present the recently defined unital algebra associated with a one-sided subshift over an arbitrary alphabet. For finite alphabets, the C*-algebraic version of this algebra coincides with the C*-algebra defined by Carlsen. We focus on infinite alphabets and show how conjugacy of two Ott-Tomforde-Willis subshifts is reflected as isomorphism of the associated algebras. Moreover, we show that the algebras are invariants for isometric conjugacy of subshifts with the product metric. This is joint work with Giuliano Boava, Gilles G. de Castro, and Daniel W. van Wyk.