Tensor products and regularity properties of Cuntz semigroups - Antoine, Ramon, 1973-; Perera, Francesc, 1970-; Thiel, Hannes, 1982- (Memoirs of the American Mathematical Society, 2018)
The Cuntz semigroup of a C^*-algebra is an important invariant in the structure and classification theory of C^*-algebras. It captures more information than K-theory but is often more delicate to handle. The authors systematically study the lattice and category theoretic aspects of Cuntz semigroups. Given a C^*-algebra A, its (concrete) Cuntz semigroup Cu(A) is an object in the category Cu of (abstract) Cuntz semigroups, as introduced by Coward, Elliott and Ivanescu. To clarify the distinction between concrete and abstract Cuntz semigroups, the authors call the latter \mathrm.