4 papers
Pure C*-algebras
Ramon Antoine, Francesc Perera, Hannes Thiel +1
We demonstrate that pure C*-algebras form a robust class by proving that pureness follows from very weak comparison and divisibility properties. Using this, we show that every simp…
Abstract Bivariant Cuntz Semigroups II
Ramon Antoine, Francesc Perera, Hannes Thiel
We previously showed that abstract Cuntz semigroups form a closed symmetric monoidal category. This automatically provides additional structure in the category, such as a compositi…
C*-algebras of stable rank one and their Cuntz semigroups
Ramon Antoine, Francesc Perera, Leonel Robert +1
The uncovering of new structure on the Cuntz semigroup of a C*-algebra of stable rank one leads to several applications: We answer affirmatively, for the class of stable rank one C…
Ideals, quotients, and continuity of the Cuntz semigroup for rings
Ramon Antoine, Pere Ara, Joan Bosa +2
In this paper we explore which part of the ideal lattice of a general ring is parametrized by its Cuntz semigroup and its ambient semigroup . We identify the…