8 citations · 16 across the 10 of their papers we have counts for
10 papers · 1 filter
Tracially reflexive C*-algebras
Laurent Cantier
Motivated by a question of L. Robert, asking whether for any separable C*-algebra A, we introduce and initiate the study of \emph{tracially reflexive…
Continuous fields of interval algebras
Laurent Cantier
This paper investigates and classifies a specific class of one-parameter continuous fields of C*-algebras, which can be seen as generalized AI-algebras. Building on the classificat…
On the Nielsen-Thomsen sequence
Laurent Cantier
The Nielsen-Thomsen sequence plays a pivotal role in refining invariants for C-algebras beyond the Elliott classification framework. This paper revisits the sequence, introduci…
Fraïssé Theory for Cuntz semigroups
Laurent Cantier, Eduard Vilalta
We introduce a Fraïssé theory for abstract Cuntz semigroups akin to the theory of Fraïssé categories developed by Kubiś. In particular, we show that any (Cuntz) Fraïssé category ha…
A systematic approach for invariants of C*-algebras
Laurent Cantier
We define a categorical framework in which we build a systematic construction that provides generic invariants for C*-algebras. The benefit is significant as we show that any invar…
Towards a classification of unitary elements of C*-algebras
Laurent Cantier
In [5] the author conjectures and partially shows that the Cuntz semigroup classifies unitary elements of unital AF-algebras. We provide a complete proof by addressing the existenc…
The unitary Cuntz semigroup on the classification of non-simple C*-algebras
Laurent Cantier
This paper argues that the unitary Cuntz semigroup, introduced in [10] and termed Cu, contains crucial information regarding the classification of non-simple C-algebras. We…
Uniformly Based Cuntz semigroups and approximate intertwinings
Laurent Cantier
We study topological aspects of the category of abstract Cuntz semigroups, termed Cu. We provide a suitable setting in which we are able to uniformly control how to approach an ele…
Unitary Cuntz semigroups of ideals and quotients
Laurent Cantier
We define a notion of ideal for objects in the category of abstract unitary Cuntz semigroups introduced in [3] and termed Cu. We show that the set of ideals of a Cu-s…
A unitary Cuntz semigroup for C*-algebras of stable rank one
Laurent Cantier
We introduce a new invariant for C*-algebras of stable rank one that merges the Cuntz semigroup information together with the K-group information. This semigroup, termed the Cu…