6 citations · 17 across the 10 of their papers we have counts for
20 papers
Super adaptable graphs and the realization problem
Pere Ara, Joan Bosa, Laurent Cantier +2
We introduce and study the family of super adaptable monoids, which includes, among many others, all conical refinement monoids that are either finitely generated, or countable, pr…
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 thes…
The dynamical Cuntz semigroup and ideal-free quotients of Cuntz semigroups
Joan Bosa, Francesc Perera, Jianchao Wu +1
We develop a theory of general quotients for W- and Cu-semigroups beyond the case of quotients by ideals. To this end, we introduce the notion of a normal pair, which allows us to…
Pure *-homomorphisms
Joan Bosa, Eduard Vilalta
We introduce and study a notion of pureness for *-homomorphisms and, more generally, for cpc. order-zero maps. After providing several examples of pureness, such as "-…
The Cuntz semigroup of a ring
Ramon Antoine, Pere Ara, Joan Bosa +2
For any ring , we introduce an invariant in the form of a partially ordered abelian semigroup built from an equivalence relation on the class of countably genera…
Stable Elements and Property (S)
Joan Bosa
We study the relation (and differences) between stability and Property (S) in the simple and stably finite framework. This leads us to characterize stable elements in terms of its…
Strict comparison for -algebras arising from Almost finite groupoids
Pere Ara, Christian Bönicke, Joan Bosa +1
In this paper we show that for an almost finite minimal ample groupoid , its reduced -algebra has real rank zero and strict comparison even though $C_r^…
The type semigroup, comparison and almost finiteness for ample groupoids
Pere Ara, Christian Bönicke, Joan Bosa +1
We prove that a minimal second countable ample groupoid has dynamical comparison if and only if its type semigroup is almost unperforated. Moreover, we investigate to what extent a…
The Realization Problem for Finitely Generated Refinement Monoids
Pere Ara, Joan Bosa, Enrique Pardo
We show that every finitely generated conical refinement monoid can be represented as the monoid of isomorphism classes of finitely generated projective modules ove…
The nuclear dimension of -stable -algebras
Joan Bosa, James Gabe, Aidan Sims +1
We show that every nuclear -stable *-homomorphism with a separable exact domain has nuclear dimension at most 1. In particular separable, nuclear, $\mathcal O_\i…
Refinement monoids and adaptable separated graphs
P. Ara, J. Bosa, E. Pardo
We define a subclass of separated graphs, the class of adaptable separated graphs, and study their associated monoids. We show that these monoids are primely generated conical refi…
The groupoids of adaptable separated graphs and their type semigroup
Pere Ara, Joan Bosa, Enrique Pardo +1
Given an adaptable separated graph, we construct an associated groupoid and explore its type semigroup. Specifically, we first attach to each adaptable separated graph a correspond…
Comparison Properties of the Cuntz semigroup and applications to C*-algebras
Joan Bosa, Henning Petzka
We study comparison properties in the category Cu aiming to lift results to the C*-algebraic setting. We introduce a new comparison property and relate it to both the CFP and -c…
A Bivariant Theory for the Cuntz Semigroup
Joan Bosa, Gabriele Tornetta, Joachim Zacharias
We introduce a bivariant version of the Cuntz semigroup as equivalence classes of order zero maps generalizing the ordinary Cuntz semigroup. The theory has many properties formally…
Reconstruction of graded groupoids from graded Steinberg algebras
Pere Ara, Joan Bosa, Roozbeh Hazrat +1
We show how to reconstruct a graded ample Hausdorff groupoid with topologically principal neutrally graded component from the ring structure of its graded Steinberg algebra over an…
Covering dimension of C*-algebras and 2-coloured classification
Joan Bosa, Nathanial P. Brown, Yasuhiko Sato +3
We introduce the concept of finitely coloured equivalence for unital *-homomorphisms between C*-algebras, for which unitary equivalence is the 1-coloured case. We use this notion t…
Open Projections and Suprema in the Cuntz Semigroup
Joan Bosa, Gabriele Tornetta, Joachim Zacharias
We provide a new and concise proof of the existence of suprema in the Cuntz semigroup using the open projection picture of the Cuntz semigroup initiated by Ortega, Rordam and Thiel…
Geometric Structure of Dimension Functions of Certain Continuous Fields
Ramon Antoine, Joan Bosa, Francesc Perera +1
In this paper we study structural properties of the Cuntz semigroup and its functionals for continuous fields of C*-algebras over finite dimensional spaces. In a variety of cases,…
The Cuntz semigroup of continuous fields
Ramon Antoine, Joan Bosa, Francesc Perera
In this paper we describe the Cuntz semigroup of continuous fields of C-algebras over one dimensional spaces whose fibers have stable rank one and trivial for each closed…
Completions of monoids with applications to the Cuntz semigroup
Ramon Antoine, Joan Bosa, Francesc Perera
We provide an abstract categorical framework that relates the Cuntz semigroups of the C-algebras and . This is done through a certain completion of or…