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Gabriel Favre: An algebraic characterization of the type I property for ample groupoids

Tid: On 2021-03-03 kl 13.15 - 14.15

Plats: Zoom, meeting ID: 685 0671 8075

Medverkande: Gabriel Favre, Stockholms universitet

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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 developping a feeling for this property, the discussion will shift to 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 Clarke. Using an explicit description of boolean inverse completion of an inverse semigroup, I will apply our result to algebraically characterize discrete inverse semigroups of type I. This is joint work with S. Raum

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