Relative Cuntz-Pimsner algebras: Gauge-invariant uniqueness theorem and the lattice of gauge-invariant ideals

Abstract: We start with an abstract definition of C*-correspondences comparing them to Fell bundles. After a first few basic results, we then swiftly move on to their representations. We introduce here the concept of covariances and relative Cuntz-Pimsner algebras.

From here we go into a detailed analysis of covariances within the category of C*-correpondences. We obtain here a systematic reduction leading us to a parametrisation of relative Cuntz-Pimsner algebras.

With this at hand we arrive at the gauge-invariant uniqueness theorem, for all (arbitrary) gauge-equivariant representations at once.

From here we move on to the analysis part of the program. We study the covariances in the case of the Fock representation and its quotients. As a result we derive that the parametrisation of relative Cuntz-Pimsner algebras is classifying. In other words, we obtain a complete and intrinsic picture of the lattice of quotients, and equivalently of gauge-invariant ideals.

If time permits, we finish off with the next chapter on their induced Fell bundles, as already investigated by Schweizer.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( slides | video )

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