Pure extension property for étale groupoid crossed products

Document Type

Presentation Abstract

Presentation Date

2-13-2020

Abstract

A state on a C*-algebra is a positive linear functional of norm 1; it's pure if it can't be written as a convex combination of other states. The GNS construction relates states to the representation theory of C*-algebras and is crucial in the study of operator algebras. If A⊂B is a unital inclusion of C*-algebras, and every pure state on A has a unique extension to a state on B, we say that A has the extension property, first identified by Kadison and Singer. In this talk I'll discuss the extension property for inclusions of the form A⊂A⋊G, where A⋊G is an étale groupoid crossed product. This covers inclusions arising from étale groupoids as well as discrete group crossed products. This work builds off work of Zarikian and relates the extension property to a groupoid action on the spectrum. I'll also discuss the related question of the almost extension property, first defined by Nagy and Reznikoff.

Additional Details

February 13, 2020 3:00 p.m. in Math 103
Refreshments time 4:00 p.m. in Math Lounge 109

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