Hannes Thiel

activity

20102025

most citedThe Cuntz Semigroup and Comparison of Open Projections

61 citations · 276 across the 37 of their papers we have counts for

collaborators

44 papers

math.OA2025

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…

math.OA2025

Rigidity of pseudofunction algebras of ample groupoids

Eusebio Gardella, Mathias Palmstrøm, Hannes Thiel

We show that a Hausdorff, ample groupoid $G$ can be completely recovered from the $I$ -norm completion of $C_{c} (G)$ . More generally, we show that this is also the…

math.OA2025

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…

math.RA2024

Fully noncentral Lie ideals and invariant additive subgroups in rings

Eusebio Gardella, Tsiu-Kwen Lee, Hannes Thiel

We prove conditions ensuring that a Lie ideal or an invariant additive subgroup in a ring contains all additive commutators. A crucial assumption is that the subgroup is fully nonc…

math.RA2024★ 1 cited

Products of commutators in matrix rings

Matej Brešar, Eusebio Gardella, Hannes Thiel

Let $R$ be a ring and let $n \geq 2$ . We discuss the question of whether every element in the matrix ring $M_{n} (R)$ is a product of (additive) commutators $[x, y] = x y - y x$ , for $x,y\in M…

math.OA2023

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…

math.OA2023★ 2 cited

Ranks of soft operators in nowhere scattered C*-algebras

M. Ali Asadi-Vasfi, Hannes Thiel, Eduard Vilalta

We show that for C*-algebras with the Global Glimm Property, the rank of every operator can be realized as the rank of a soft operator, that is, an element whose hereditary sub-C*-…

math.OA2023

Prime ideals in C*-algebras and applications to Lie theory

Eusebio Gardella, Hannes Thiel

We show that every proper, dense ideal in a C*-algebra is contained in a prime ideal. It follows that a subset generates a C*-algebra as a not necessarily closed ideal if and only…

math.OA2023

Soft operators in C*-algebras

Hannes Thiel, Eduard Vilalta

We say that a C*-algebra is soft if it has no nonzero unital quotients, and we connect this property to the Hjelmborg-Rørdam condition for stability and to property (S) of Ortega-P…

math.OA2023

Traces on ultrapowers of C*-algebras

Ramon Antoine, Francesc Perera, Leonel Robert +1

Using Cuntz semigroup techniques, we characterize when limit traces are dense in the space of all traces on a free ultrapower of a C*-algebra. More generally, we consider density o…

math.RA2023

Rings and C*-algebras generated by commutators

Eusebio Gardella, Hannes Thiel

We show that a unital ring is generated by its commutators as an ideal if and only if there exists a natural number $N$ such that every element is a sum of $N$ products of pairs of…

math.RA2022

Zero-product balanced algebras

Eusebio Gardella, Hannes Thiel

We say that an algebra is zero-product balanced if $ab \otimes c$ and $a \otimes b c$ agree modulo tensors of elements with zero-product. This is closely related to but more general t…

math.OA2022

The Global Glimm Property

Hannes Thiel, Eduard Vilalta

It is known that a C*-algebra with the Global Glimm Property is nowhere scattered (it has no elementary ideal-quotients), and the Global Glimm Problem asks if the converse holds. W…

math.OA2022

Weighted homomorphisms between C*-algebras

Eusebio Gardella, Hannes Thiel

We show that a bounded, linear map between C*-algebras is a weighted $*$ -homomorphism (the central compression of a $*$ -homomorphism) if and only if it preserves zero-product…

math.OA2021

Nowhere scattered C*-algebras

Hannes Thiel, Eduard Vilalta

We say that a C*-algebra is nowhere scattered if none of its quotients contains a minimal open projection. We characterize this property in various ways, by topological properties…

math.OA2021

Covering dimension of Cuntz semigroups II

Hannes Thiel, Eduard Vilalta

We show that the dimension of the Cuntz semigroup of a C*-algebra is determined by the dimensions of the Cuntz semigroups of its separable sub-C*-algebras. This allows us to remove…

math.OA2021

Covering dimension of Cuntz semigroups

Hannes Thiel, Eduard Vilalta

We introduce a notion of covering dimension for Cuntz semigroups of C*-algebras. This dimension is always bounded by the nuclear dimension of the C*-algebra, and for subhomogeneous…

math.OA2020★ 1 cited

Diffuse traces and Haar unitaries

Hannes Thiel

We show that a tracial state on a unital C*-algebra admits a Haar unitary if and only if it is diffuse, if and only if it does not dominate a tracial functional that factors throug…

math.OA2020

Generators in $Z$ -stable C*-algebras of real rank zero

Hannes Thiel

We show that every separable C*-algebra of real rank zero that tensorially absorbs the Jiang-Su algebra contains a dense set of generators. It follows that in every classifiable, s…

math.OA2020

The generator rank of subhomogeneous C*-algebras

Hannes Thiel

We compute the generator rank of a subhomgeneous C*-algebra in terms of the covering dimension of the pieces of its primitive ideal space corresponding to irreducible representatio…

math.OA2019★ 2 cited

Edwards' condition for quasitraces on C*-algebras

Ramon Antoine, Francesc Perera, Leonel Robert +1

We prove that Cuntz semigroups of C*-algebras satisfy Edwards' condition with respect to every quasitrace. This condition is a key ingredient in the study of the realization proble…

math.OA2019★ 12 cited

Rigidity results for $L^{p}$ -operator algebras and applications

Yemon Choi, Eusebio Gardella, Hannes Thiel

For $p \in [1, \infty)$ , we show that every unital $L^{p}$ -operator algebra contains a unique maximal $C^{*}$ -subalgebra, which is always abelian if $p \neq = 2$ . Using this, we canonically…

math.OA2019★ 14 cited

Cuntz semigroups of ultraproduct C*-algebras

Ramon Antoine, Francesc Perera, Hannes Thiel

We prove that the category of abstract Cuntz semigroups is bicomplete. As a consequence, the category admits products and ultraproducts. We further show that the scaled Cuntz semig…

math.OA2018

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…

Topological full groups, invertible isometries, and automorphisms of groupoid algebras

Rigidity of pseudofunction algebras of ample groupoids

Prime and semiprime Lie ideals in C*-algebras

Fully noncentral Lie ideals and invariant additive subgroups in rings

Products of commutators in matrix rings

Semiprime ideals in C*-algebras

Ranks of soft operators in nowhere scattered C*-algebras

Prime ideals in C*-algebras and applications to Lie theory

Soft operators in C*-algebras

Traces on ultrapowers of C*-algebras

Rings and C*-algebras generated by commutators

Zero-product balanced algebras

The Global Glimm Property

Weighted homomorphisms between C*-algebras

Nowhere scattered C*-algebras

Covering dimension of Cuntz semigroups II

Covering dimension of Cuntz semigroups

Diffuse traces and Haar unitaries

Generators in Z-stable C*-algebras of real rank zero

The generator rank of subhomogeneous C*-algebras

Edwards' condition for quasitraces on C*-algebras

Rigidity results for Lp-operator algebras and applications

Cuntz semigroups of ultraproduct C*-algebras

Abstract Bivariant Cuntz Semigroups II

Generators in $Z$ -stable C*-algebras of real rank zero

Rigidity results for $L^{p}$ -operator algebras and applications