Cuntz-Pimsner algebras were introduced by Pimsner in the '90s, as generalization of both Cuntz-Krieger algebras and crossed products by the integers. The underlying mathematical object behind Pimsner's construction is a C*-correspondence over a C*-algebra. Of particular interest are Cuntz-Pimsner algebras arising from full, minimal, non-periodic, and finitely generated projective C*-correspondence over commutative C*-algebras. A large class of such examples is obtained by considering the set $\Gamma(V,\alpha)$ of continuous sections of a complex vector bundle V on a compact metric space X, where left multiplication is given by a twist by a homeomorphism $\alpha\colon X\to X$.

The talk will focus on the structural properties and classification of Cuntz-Pimsner algebras associated with this class of C*-correspondences, in the case when $\alpha$ is a minimal homeomorphism.

In the case of crossed products by minimal homeomorphisms, the orbit-breaking subalgebra, defined by I. Putnam, is a large subalgebra in the sense of N. C. Phillips. Orbit-breaking subalgebras can also be defined in the context of Cunts-Pimsner algebras associated to correspondences of the form $\Gamma(V,\alpha)$. We show that when V is a line bundle, the orbit-breaking subalgebra is a centrally large subalgebra. Moreover, when X has finite covering dimension, the orbit-breaking subalgebra is classifiable.

This is joint work with M. S. Adamo, D. Archey, M. Georgescu, M. Forough, J. A Jeong, and K. Strung.

Bio: Maria Grazia Viola is an associate professor in the Department of Mathematical Sciences at Lakehead University. Prior to that she was at postdoctoral fellow at Texas A&M University and Queen University. Her research interests are classification of C*-algebras, C*-algebras non-isomorphic to their opposite algebras, free probability, subfactor theory, and L^p operator algebras.