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AF-action groupoid models for diagonal AH-algebras
Ali Imad Raad, Jonathan Taylor
We show that an inductive AH-system with diagonal connecting maps describes an action of the canonical AF-groupoid on the spectrum of the canonical C-diagonal, and that the can…
C-diagonals in AH-algebras arising from generalized diagonal connecting maps: spectrum and uniqueness
Ali Imad Raad
We associate a Bratteli-type diagram to AH-algebras arising from generalized diagonal connecting maps. We use this diagram to give an explicit description of the connected componen…
Inductive Limits of Noncommutative Cartan Inclusions
Ralf Meyer, Ali Imad Raad, Jonathan Taylor
We prove that an inductive limit of aperiodic noncommutative Cartan inclusions is a noncommutative Cartan inclusion whenever the connecting maps are injective, preserve normalisers…
Constructing C*-diagonals in AH-algebras
Xin Li, Ali Imad Raad
We construct Cartan subalgebras and hence groupoid models for classes of AH-algebras. Our results cover all AH-algebras whose building blocks have base spaces of dimension at most…
A Generalization of Renault's Theorem for Cartan Subalgebras
Ali Imad Raad
We prove a generalized version of Renault's theorem for Cartan subalgebras. We show that the original assumptions of second countability and separability are not needed. This weake…