Irreducible representations of one-sided subshift algebras
Rings and Algebras
2023-06-29 v1 Dynamical Systems
Operator Algebras
Abstract
Given a subshift over an arbitrary alphabet, we construct a representation of the associated unital algebra. We describe a criteria for the faithfulness of this representation in terms of the existence of cycles with no exits. Subsequently, we focus on describing the irreducible components of this representation and characterize equivalence between such components. Building upon these findings, we identify the minimal left ideals of a subshift algebra associated with (what we call) line paths.
Keywords
Cite
@article{arxiv.2306.16179,
title = {Irreducible representations of one-sided subshift algebras},
author = {Daniel Gonçalves and Danilo Royer},
journal= {arXiv preprint arXiv:2306.16179},
year = {2023}
}