On the inverse hull of a Markov shift

TL;DR

This paper characterizes the inverse hulls of semigroups from Markov shifts and shows that non-conjugate shifts can have isomorphic inverse hulls, revealing new structural insights.

Contribution

It provides an abstract characterization of inverse hulls for semigroups from Markov shifts and demonstrates their potential to be isomorphic despite non-conjugacy.

Findings

Inverse hulls can be isomorphic for non-conjugate Markov shifts

Provides an abstract framework for inverse hulls of Markov shift semigroups

Shows limitations of inverse hulls in distinguishing Markov shifts

Abstract

In this paper we provide an abstract characterization of the inverse hulls of semigroups associated with Markov shifts. As an application of the characterization we give an example of Markov shifts that are not conjugate, but have isomorphic inverse hulls.