Semi-Cartan subalgebras and twisted groupoid C*-algebras

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• Lisa Orloff Clark (Victoria University of Wellington)
• Thursday 17 July 2025, 11:15-11:55
• External.

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TGAW02 - C*-algebras: classification and dynamical constructions

We introduce the notion of semi-Cartan C-subalgebras, which are commutative subalgebras that, unlike Cartan subalgebras, are not required to be maximal abelian. Despite this relaxation, they retain enough structure to fully characterize a broad class of C-algebras arising from groupoids. Specifically, we show that a C-algebra contains a semi-Cartan subalgebra if and only if it is isomorphic to a twisted étale groupoid C-algebra, possibly nonreduced and associated to a noneffective groupoid. This generalizes the Kumjian–Renault framework.This is joint work with Tristan Bice, Ying-Fen Lin, and Kathryn McCormick.

This talk is part of the Isaac Newton Institute Seminar Series series.

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