University of the Faroe Islands

output

20082024

most citedEquivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph C*-algebras and Leavitt path algebras

58 citations

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

collaborating institutions

Showing math.OAShow all

27 papers · 1 filter

math.OA2021★ 11 cited

Conjugacy of local homeomorphisms via groupoids and C*-algebras

Becky Armstrong, Kevin Aguyar Brix, Toke Meier Carlsen +1

We investigate dynamical systems consisting of a locally compact Hausdorff space equipped with a partially defined local homeomorphism. Important examples of such systems include s…

math.OA2020★ 9 cited

Shift equivalences through the lens of Cuntz-Krieger algebras

Toke Meier Carlsen, Adam Dor-On, Søren Eilers

Motivated by Williams' problem of measuring novel differences between shift equivalence (SE) and strong shift equivalence (SSE), we introduce three equivalence relations that provi…

math.OA2019★ 6 cited

Gauge-invariant ideals of C*-algebras of Boolean dynamical systems

Toke Meier Carlsen, Eun Ji Kang

We enlarge the class of $C^{*}$ -algebras of Boolean dynamical systems in order to include all weakly left-resolving normal labelled space $C^{*}$ -algebras in it. We prove a gauge-invar…

math.OA2019★ 4 cited

Condition (K) for Boolean dynamical systems

Toke Meier Carlsen, Eun Ji Kang

We generalize Condition (K) from directed graphs to Boolean dynamical systems and show that a locally finite Boolean dynamical system $(B, L, θ)$ with countable $…

math.OA2019★ 10 cited

C*-algebras, groupoids and covers of shift spaces

Kevin Aguyar Brix, Toke Meier Carlsen

To every one-sided shift space $X$ we associate a cover $X ~$ , a groupoid $G_{X}$ and a $C^{*}$ -algebra $O_{X}$ …

math.OA2019★ 2 cited

Orbit equivalence of higher-rank graphs

Toke Meier Carlsen, James Rout

We study the notions of continuous orbit equivalence and eventual one-sided conjugacy of finitely-aligned higher-rank graphs and two-sided conjugacy of row-finite higher-rank graph…

math.OA2018★ 3 cited

Topological freeness for $C^{*}$ -correspondences

T. M. Carlsen, B. K. Kwasniewski, E. Ortega

We study conditions that ensure uniqueness theorems of Cuntz-Krieger type for relative Cuntz-Pimsner algebras $O (J, X)$ associated to a $C^{*}$ -correspondence $X$ over a $C^…

math.OA2017★ 15 cited

Cuntz-Krieger algebras and one-sided conjugacy of shifts of finite type and their groupoids

Kevin Aguyar Brix, Toke Meier Carlsen

A one-sided shift of finite type $(X_{A}, σ_{A})$ determines on the one hand a Cuntz-Krieger algebra $O_{A}$ with a distinguished abelian subalgebra $D_{A}$ and a certai…

math.OA2017★ 38 cited

Reconstruction of groupoids and C*-rigidity of dynamical systems

Toke Meier Carlsen, Efren Ruiz, Aidan Sims +1

We show how to construct a graded locally compact Hausdorff étale groupoid from a C*-algebra carrying a coaction of a discrete group, together with a suitable abelian subalgebra. W…

math.OA2016★ 45 cited

The complete classification of unital graph $C^{*}$ -algebras: Geometric and strong

Søren Eilers, Gunnar Restorff, Efren Ruiz +1

We provide a complete classification of the class of unital graph $C^{*}$ -algebras - prominently containing the full family of Cuntz-Krieger algebras - showing that Morita equivalenc…

math.OA2016★ 41 cited

Diagonal-preserving gauge-invariant isomorphisms of graph $C^{*}$ -algebras

Toke Meier Carlsen, James Rout

We study graph $C^{*}$ -algebras equipped with generalised gauge actions, and characterise in terms of groupoids and groupoid cocycles when two graph $C^{*}$ -algebras are isomorphic by…

math.OA2016★ 6 cited

Strong classification of purely infinite Cuntz-Krieger algebras

Toke Meier Carlsen, Gunnar Restorff, Efren Ruiz

In 2006, Restorff completed the classification of all Cuntz-Krieger algebras with finitely many ideals (i.e., those that are purely infinite) up to stable isomorphism. He left open…

math.OA2016★ 41 cited

Geometric classification of graph $C^{*}$ -algebras over finite graphs

Søren Eilers, Gunnar Restorff, Efren Ruiz +1

We address the classification problem for graph $C^{*}$ -algebras of finite graphs (finitely many edges and vertices), containing the class of Cuntz-Krieger algebras as a prominent sp…

math.OA2016★ 4 cited

Invariance of the Cuntz splice

Søren Eilers, Gunnar Restorff, Efren Ruiz +1

We show that the Cuntz splice induces stably isomorphic graph $C^{*}$ -algebras.

math.OA2016★ 58 cited

Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph C*-algebras and Leavitt path algebras

Toke Meier Carlsen, Efren Ruiz, Aidan Sims

We prove that ample groupoids with sigma-compact unit spaces are equivalent if and only if they are stably isomorphic in an appropriate sense, and relate this to Matui's notion of…

math.OA2015★ 6 cited

On Hong and Szymanski's description of the primitive-ideal space of a graph algebra

Toke Meier Carlsen, Aidan Sims

In 2004, Hong and Szymanski gave a complete description of the primitive-ideal space of the C*-algebra of a directed graph. This article details a slightly different approach, in t…

math.OA2015★ 20 cited

$C^{*}$ -algebras associated to Boolean dynamical systems

Toke Meier Carlsen, Eduard Ortega, Enrique Pardo

The goal of these notes is to present the C*-algebra $C^{*} (B, L, θ)$ of a Boolean dynamical system $(B, L, θ)$ , that generalizes the $C^{*}$ -algebra associated to Labelled graphs introduc…

math.OA2015★ 1 cited

Corrigendum to "Classifying C*-algebras with both finite and infinite subquotients"

Søren Eilers, Gunnar Restorff, Efren Ruiz

As recently pointed out by Gabe, a fundamental paper by Elliott and Kucerovsky concerning the absorption theory for C*-algebras contains an error, and as a consequence we must repo…

math.OA2014★ 7 cited

Classification of real rank zero, purely infinite C*-algebras with at most four primitive ideals

Sara E. Arklint, Gunnar Restorff, Efren Ruiz

Counterexamples to classification of purely infinite, nuclear, separable C*-algebras (in the ideal-related bootstrap class) and with primitive ideal space X using ideal-related K-t…

math.OA2013★ 43 cited

Partial actions and KMS states on relative graph $C^{*}$ -algebras

Toke M. Carlsen, Nadia S. Larsen

The relative graph $C^{*}$ -algebras introduced by Muhly and Tomforde are generalizations of both graph algebras and their Toeplitz extensions. For an arbitrary graph $E$ and a subset…

math.OA2013★ 2 cited

Automorphisms of Cuntz-Krieger algebras

Søren Eilers, Gunnar Restorff, Efren Ruiz

We prove that the natural homomorphism from Kirchberg's ideal-related KK-theory, KKE(e, e'), with one specified ideal, into Hom_Λ (\underline{K}_{E} (e), \underline{K}_{E} (e')) is…

math.OA2012★ 5 cited

Classification of graph C*-algebras with no more than four primitive ideals

Søren Eilers, Gunnar Restorff, Efren Ruiz

We describe the status quo of the classification problem of graph C*-algebras with four primitive ideals or less.

math.OA2012★ 6 cited

Projective dimension in filtrated K-theory

Rasmus Bentmann

Under mild assumptions, we characterise modules with projective resolutions of length n in the target category of filtrated K-theory over a finite topological space in terms of two…

math.OA2011★ 6 cited

Filtrated K-theory for real rank zero C*-algebras

Sara Arklint, Gunnar Restorff, Efren Ruiz

Using Kirchberg KK_X-classification of purely infinite, separable, stable, nuclear C*-algebras with finite primitive ideal space, Bentmann showed that filtrated K-theory classifies…

Conjugacy of local homeomorphisms via groupoids and C*-algebras

Shift equivalences through the lens of Cuntz-Krieger algebras

Gauge-invariant ideals of C*-algebras of Boolean dynamical systems

Condition (K) for Boolean dynamical systems

C*-algebras, groupoids and covers of shift spaces

Orbit equivalence of higher-rank graphs

Topological freeness for C∗-correspondences

Cuntz-Krieger algebras and one-sided conjugacy of shifts of finite type and their groupoids

Reconstruction of groupoids and C*-rigidity of dynamical systems

The complete classification of unital graph C∗-algebras: Geometric and strong

Diagonal-preserving gauge-invariant isomorphisms of graph C∗-algebras

Strong classification of purely infinite Cuntz-Krieger algebras

Geometric classification of graph C∗-algebras over finite graphs

Invariance of the Cuntz splice

Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph C*-algebras and Leavitt path algebras

On Hong and Szymanski's description of the primitive-ideal space of a graph algebra

C∗-algebras associated to Boolean dynamical systems

Corrigendum to "Classifying C*-algebras with both finite and infinite subquotients"

Classification of real rank zero, purely infinite C*-algebras with at most four primitive ideals

Partial actions and KMS states on relative graph C∗-algebras

Automorphisms of Cuntz-Krieger algebras

Classification of graph C*-algebras with no more than four primitive ideals

Projective dimension in filtrated K-theory

Filtrated K-theory for real rank zero C*-algebras

Topological freeness for $C^{*}$ -correspondences

The complete classification of unital graph $C^{*}$ -algebras: Geometric and strong

Diagonal-preserving gauge-invariant isomorphisms of graph $C^{*}$ -algebras

Geometric classification of graph $C^{*}$ -algebras over finite graphs

$C^{*}$ -algebras associated to Boolean dynamical systems

Partial actions and KMS states on relative graph $C^{*}$ -algebras