AMENABILITY OF NON-HAUSDORFF ÉTALE GROUPOIDS AND NUCLEARITY OF THEIR C*-ALGEBRAS

Prelegent(ci)

ALCIDES BUSS

Afiliacja

Universidade Federal de Santa Catarina, Florianópolis, Brazil

Język referatu

angielski

Termin

23 kwietnia 2025 17:15

Informacje na temat wydarzenia

IMPAN 405 & ZOOM

Tytuł w języku polskim

AMENABILITY OF NON-HAUSDORFF ÉTALE GROUPOIDS AND NUCLEARITY OF THEIR C*-ALGEBRAS

Seminarium

North Atlantic Noncommutative Geometry Seminar

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The link between amenability and nuclearity lies at the heart of many structural results in operator algebras. For discrete groups, these notions are famously equivalent via the reduced group C*-algebra. In this talk, I will explore how this correspondence extends to étale groupoids, even in the presence of a non-Hausdorff topology, where the classical theory encounters subtle complications. Focusing on both the usual reduced groupoid C*-algebra and the Borel version built from bounded measurable functions, I will show that the amenability of a groupoid is equivalent to the nuclearity of both of these algebras. This provides a stable analytic characterization of amenability that remains robust under topological pathologies. I will also touch on the notion of essential amenability and the associated essential C*-algebra, noting that some technical issues remain unresolved in that setting, and highlighting the utility of Borel methods as a workaround. Applications include Bruce-Li algebras arising from semigroup actions, which serve as concrete and interesting examples of the theory at work. This talk is based on joint work (in progress) with Diego Martínez.

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