[AN] Francesca Arici: KK duality for Temperley—Lieb subproduct systems

03 December 2024 16:00 till 17:00 - Location: EEMCS Lecture Hall F | Add to my calendar

The notion of KK-duality is a noncommutative analogue of the Spanier–Whitehead duality. It induces natural isomorphisms between the K-theory and K-homology of the dual C∗-algebras. Notable examples of noncommutative C*-algebras satisfying KK-duality are Cuntz—Krieger algebras.
In this talk, we will describe a quantum analogue of the result of Kaminker and Putnam on Cuntz—Krieger algebras. Specifically, we consider the Cuntz—Pimsner algebras of subproduct systems defined by Temperley–Lieb polynomials, as defined by Habbestad—Neshveyev. These algebras can be thought of as algebras of functions on algebraic subsets of noncommutative spheres. Joint work with D. Gerontogiannis and S. Neshveyev.