Existence and Uniqueness of Canonical Cartan Subalgebras in Inductive Limit C*-algebras

Abstract: Cartan subalgebras of C*-algebras have witnessed major breakthroughs recently, becoming the cornerstone of how to build a bridge between C*-algebras on the one hand, and geometric group theory and topological dynamics on the other. As such, existence and uniqueness questions become crucial.

In this talk I will introduce the notion of a Cartan subalgebra and discuss the question of existence and uniqueness in the setting of inductive limit C*-algebras. Indeed Stratila and Voiculescu show in 1975 that AF-algebras admit a canonical Cartan subalgebra. I will provide a novel uniqueness result for the uniqueness of these subalgebras in AF-algebras, and also completely settle the question of existence and uniqueness of canonical Cartan subalgebras in AI-algebras and AT-algebras. If time permits, I will generalize a theorem of Renault's that gives a correspondence between Cartan pairs and C*-algebras of twisted étale groupoids.

functional analysisgroup theoryoperator algebrasquantum algebra

Audience: researchers in the topic

Groups, Operators, and Banach Algebras Webinar

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