Q-Math Seminar
The Cuntz semigroup of C*-algebras and pureness
Speaker: Francesc Perera (Universitat Autònoma de Barcelona)Date: Tuesday, 21 April 2026 - 12:00Place: Aula Naranja, ICMAT
Abstract:
In this talk I will define the Cuntz semigroup of a C*-algebra as an analogue of the Murray-von Neumann semigroup of idempotents. I will give some classes of examples where the semigroup is computable and indicate its importance for the classification program. In the second part of the talk I will focus on certain order properties of the semigroup that yield the notion of pureness, a property that plays a prominent role in the structure of C*-algebras, and it can be thought of as tensorial absorption at the level of the semigroup by the so-called Jiang-Su algebra. Part of the talk is joint work with Ramon Antoine, Hannes Thiel, and Eduard Vilalta.
