AG Mathematische Physik, Francesca Arici (Leiden): KK duality for Temperley—Lieb subproduct systems

Francesca Arici (Leiden)

KK duality for Temperley—Lieb subproduct systems

Abstract:

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.