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<p>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.</p>

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Irreducible Representations of One-Sided Subshift Algebras

  • 期刊论文

  • 发表日期：

    2025年8月28日

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  • Daniel Gonçalves,
  • Danilo Royer

摘要

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.