Cartan subalgebras of C*-algebras associated with iterated function systems

2025/01/07 by Ito, Kei
#46L55 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2501.04127

Abstract

Let X be a compact Hausdorff space, and let γ be an iterated function system on X. Kajiwara and Watatani showed that if γ is self-similar and satisfies the open set condition and some additional technical conditions, C(X) is a maximal abelian subalgebra of the Kajiwara--Watatani algebra Ø_γ associated with γ. In this paper, we extend their results by providing sufficient conditions under which C(X) becomes a Cartan subalgebra of Ø_γ. Additionally, we present sufficient conditions under which C(X) fails to be a masa of Ø_γ.

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