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A Cuntz--Krieger Uniqueness theorem for C*-algebras of relative generalized Boolean dynamical systems (2305.09232v1)

Published 16 May 2023 in math.OA

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.

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