Irreducible representations of one-sided subshift algebras

2023/06/28 by Gonçalves, Daniel, Royer, Danilo · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2306.16179

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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• The Leavitt inverse semigroup of a separated graph

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• Algebras of one-sided subshifts over arbitrary alphabets
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• C*-Algebras of one-sided subshifts over arbitrary alphabets
• Irreducible components of varieties of representations II
• Irreducible and permutative representations of ultragraph Leavitt path algebras