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

TL;DR
This paper investigates conditions under which the algebra of continuous functions on a compact space forms a Cartan subalgebra within the Kajiwara--Watatani algebra associated with an iterated function system, extending previous results.
Contribution
It provides new sufficient conditions for $C(X)$ to be a Cartan subalgebra or fail to be a maximal abelian subalgebra in the associated algebra.
Findings
$C(X)$ is a Cartan subalgebra under certain conditions.
$C(X)$ may not be a masa if specific criteria are not met.
Extended the class of iterated function systems where these properties hold.
Abstract
Let be a compact Hausdorff space, and let be an iterated function system on . Kajiwara and Watatani showed that if is self-similar and satisfies the open set condition and some additional technical conditions, is a maximal abelian subalgebra of the Kajiwara--Watatani algebra associated with . In this paper, we extend their results by providing sufficient conditions under which becomes a Cartan subalgebra of . Additionally, we present sufficient conditions under which fails to be a masa of .
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Mathematical Analysis and Transform Methods
