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arXiv · 2306.16179

Irreducible representations of one-sided subshift algebras

Daniel Gonçalves·Danilo Royer
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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.

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Daniel Gonçalves, Danilo Royer. 2023-06-28. Irreducible representations of one-sided subshift algebras. https://arxiv.org/abs/2306.16179

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