Set Theory & Analysis

Cuntz-Pimsner algebras associated to finite rank vector bundles twisted by a minimal homeomorphism

Maria Stella Adamo

Tuesday, 8. September 2020 - 10:00 to 11:30

We discuss structural properties of Cuntz-Pimsner algebras arising by continuous sections Γ(V, φ)

of a complex finite rank vector bundle V on a compact metric space X twisted by a minimal

homeomorphism φ : X → X. In this context, we consider ”large enough” C*-subalgebras capturing

fundamental properties of the containing Cuntz-Pimsner algebra. Then we will examine conditions

when these C*-algebras can be classified using the Elliott invariant.

In the case of a line bundle, in addition, we are interested in studying the topological full group

for the minimal dynamical system (X, φ), that will shed light on an isomorphism theorem for the

associated Cuntz-Pimsner algebras.

The first part is joint work in progress with Archey, Forough, Georgescu, Jeong, Strung, Viola,

while the second part is joint work in progress with Forough, Strung.

of a complex finite rank vector bundle V on a compact metric space X twisted by a minimal

homeomorphism φ : X → X. In this context, we consider ”large enough” C*-subalgebras capturing

fundamental properties of the containing Cuntz-Pimsner algebra. Then we will examine conditions

when these C*-algebras can be classified using the Elliott invariant.

In the case of a line bundle, in addition, we are interested in studying the topological full group

for the minimal dynamical system (X, φ), that will shed light on an isomorphism theorem for the

associated Cuntz-Pimsner algebras.

The first part is joint work in progress with Archey, Forough, Georgescu, Jeong, Strung, Viola,

while the second part is joint work in progress with Forough, Strung.

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