An Algebraic Characterization of the Type I Property for Ample Groupoids

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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