Relative ultragraph algebras and infinite interval maps

TL;DR

This paper introduces relative ultragraph algebras, extending classical injectivity criteria, and connects them to the dynamics of infinite Markov interval maps, providing a framework for their representations.

Contribution

It defines relative ultragraph algebras and extends injectivity criteria to this setting, motivated by the dynamics of infinite Markov maps.

Findings

Established a new class of algebras linked to infinite interval maps

Extended classical injectivity criteria to the relative ultragraph algebra setting

Provided a framework for representations induced by infinite Markov maps

Abstract

In this paper, we introduce the notion of relative ultragraph algebras and extend classical injectivity criteria for representations, particularly those arising from branching systems,to this relative setting. This new concept is closely connected to, and indeed motivated by, the dynamics of certain interval maps that we call infinite Markov maps. The central point is that these algebras provide the natural framework in which representations induced by such maps are defined.