UK Virtual Operator Algebras Seminar: An introduction to Cuntz--Pimsner algebras

Francesca Arici (Universiteit Leiden)

Thursday 14th May, 2020 16:00-16:45 Contact Mike.Whittaker@glasgow.ac.uk for Zoom info

Abstract

In 1997 Pimsner described how to construct two universal C*-algebras associated with an injective C*-correspondence, now known as the Toeplitz--Pimsner and Cuntz--Pimsner algebras. In this talk I will recall their construction, focusing for simplicity on the case of a finitely generated projective correspondence. I will describe the associated six-term exact sequence in K(K)-theory and explain how these can be used in practice for computational purposes. Finally, I will describe how, in the case of a self-Morita equivalence, these exact sequences can be interpreted as an operator algebraic version of the classical Gysin sequence for circle bundles.

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