An introduction to Cuntz--Pimsner algebras

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. Assumed Knowledge: Elementary C*-algebra theory.

operator algebras

Audience: researchers in the topic

UK Virtual operator algebras seminar

Series comments: Due to the Coronavirus crisis we have created an online seminar on the Zoom platform meeting fortnightly on Thursdays at 4pm. The Zoom coordinates are announced using our mailing list, please contact one of the seminar organisers to have your name added to the mailing list.

Our aim is to host talks which are more expository than a typical research talk might be. We plan to invite experts in their field to present introductions to their areas of research, expositions of key proof techniques or constructions, or perhaps sketching the background required to appreciate recent breakthroughs. We hope talks will be widely accessible to graduate students and postdocs, as well as established researchers.

We have made the decision to not publish video links directly to the web. Rather, we ask that if you are interested, you join the seminar mailing list. Zoom link and meeting IDs will always be sent out on the mailing list shortly before each seminar.

Please contact one of the organisers to be added to the seminar mailing list so we can send you the Zoom link and meeting ID.