7 papers · 1 filter
Topological full groups, invertible isometries, and automorphisms of groupoid algebras
Eusebio Gardella, Mathias Palmstrøm, Hannes Thiel
We show that the topological full group of a Hausdorff ample groupoid with compact unit space coincides with the group of homotopy classes of invertible isometries in pseudofunctio…
Prime and semiprime Lie ideals in C*-algebras
Eusebio Gardella, Kan Kitamura, Hannes Thiel
Using the theory of Dixmier ideals developed in previous work, we show that every semiprime Lie ideal in a C*-algebra arises as the full normalizer subspace of a semiprime two-side…
Rigidity of pseudofunction algebras of ample groupoids
Eusebio Gardella, Mathias Palmstrøm, Hannes Thiel
We show that a Hausdorff, ample groupoid can be completely recovered from the -norm completion of . More generally, we show that this is also the…
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…
Semiprime ideals in C*-algebras
Eusebio Gardella, Kan Kitamura, Hannes Thiel
We show that a not necessarily closed ideal in a C*-algebra is semiprime if and only if it is idempotent, if and only if it is closed under square roots of positive elements. Among…