An Algebraic Characterization of the Type I Property for Ample Groupoids
Gabriel Favre (University of Stockholm)
Abstract: I will discuss the type I property for second countable locally compact Hausdorff ample groupoids. Loosely speaking, the type I property says that the von Neumann algebras generated by unitary representations are the simplest possible kind of von Neumann algebras to understand. After developing a feel for this property, the discussion will shift towards the noncommutative Stone duality between ample groupoids and Boolean inverse semigroups. This duality is used in a new characterization of the type I property for groupoids, that we obtained. This characterization will appear as the semigroup counterpart to a result of van Wyk. If time permits, I will apply our result to algebraically characterize discrete inverse semigroups of type I. This is joint work with S. Raum.
functional analysisgroup theoryoperator algebrasquantum algebra
Audience: researchers in the topic
Groups, Operators, and Banach Algebras Webinar
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Organizers: | Jared White*, Ulrik Enstad, Bence Horvath |
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