Bartosz K. Kwaśniewski: Topological aperiodicity for product systems of C*-correspondences

Bartosz K. Kwaśniewski (University of Southern Denmark, Odense) will talk on: Topological aperiodicity for product systems of C*-correspondences

Abstract:We introduce a semigroup of multivalued maps dual to a product system of $C^*$-correspondences over an Ore semigroup. Under a certain aperiodicity condition on the dual semigroup we obtain a uniqueness theorem and a simplicity criterion for the associated Cuntz-Pimsner algebra. These results generalize similar statements for crossed products by groups (R. J. Archbold, J. S. Spielberg) and Exel’s crossed products (R. Exel, A. Vershik). They also give interesting conditions for topological higher rank graphs, and apply to the new Cuntz $C^*$-algebra $\mathcal{Q}_\mathbb{N}$ arising from the `$ax+b$'-semigroup over natural numbers. (Based on joint work with Wojciech Szymański.)