Operator Algebra Seminar

Abstract: In this talk I will draft the construction of a semigroup S(R)$ that can be attached to any ring R. The construction is inspired by the one developed by Coward, Elliott, and Ivanescu for C*-algebras, uses countably generated projective modules –in substitution of countably generated Hilbert modules–, and also a suitable equivalence relation. I will discuss how this semigroup relates to the usual Cuntz semigroup Cu(A) for a C*-algebra A, and identify a class of rings for which we can ensure that S(R) belongs to the category of abstract Cuntz semigroups. Some intriguing questions for C*-algebras arise in this setting, that I will discuss if time allows. Part of this is joint work with Ramon Antoine, Pere Ara, Joan Bosa, and Eudard Vilalta, and also with Ramon Antoine, Laurent Cantier, and Guillem Quingles.