A Cuntz--Krieger Uniqueness theorem for C*-algebras of relative generalized Boolean dynamical systems

2023/05/16 by Toke Meier Carlsen, Carlsen, Toke Meier, Eun Ji Kang +1 · 1 citation
Computer Science · Mathematics · #46L05 ( secondary) #46L55(primary) 37B99 #Advanced Algebra and Logic #Advanced Operator Algebra Research #FOS: Mathematics #Functional Equations Stability Results #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2305.09232

openalex publication_date 2023/05/16 · openalex created_date 2023/05/18 · openalex updated_date 2026/07/28

Abstract

We prove a version of the Cuntz--Krieger Uniqueness Theorem for C^*-algebras of arbitrary relative generalized Boolean dynamical systems. We then describe properties of a C^*-algebra of a relative generalized Boolean dynamical system when the underlying Boolean dynamical system satisfies Condition (K). We also define a notion of minimality of a Boolean dynamical system and give sufficient and necessary conditions for the minimality. Using these results, we characterize the generalized Boolean dynamical systems who's C^*-algebra is simple.

Cited by

• K-Theory and Structural Properties of C^*-Algebras Associated with Relative Generalized Boolean Dynamical Systems

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