Tron Omland

activity

20092026

most citedOn the K-theory of C*-algebras arising from integral dynamics

21 citations · 82 across the 27 of their papers we have counts for

collaborators

30 papers

math.OA2026

$Z$ -stable and selfless inclusions for the infinite braid group

Tron Omland

Let $B_{\infty}$ and $P_{\infty}$ be the braid group and the pure braid group on infinitely many strands. We show that the inclusion $C_{r}^{*} (P_{\infty}) \subseteq C_{r}^{*} (B_{\infty})$ is $\mat…

quant-ph2026

Universal Quantum Computation with Multi-Mode Schrödinger Cat States Stabilized by Non-Local Dissipation Engineering

Jesper Lind-Olsen, Jonas Lidal, Tron Omland +1

Schrödinger cat states provide a hardware-efficient platform for bosonic quantum error correction by encoding logical information in protected manifolds of harmonic oscillators. Wh…

math.OA2026

Selflessness for twisted group C*-algebras of amenable groups and their inclusions

Tron Omland

For a discrete amenable group $G$ with a two-cocycle $σ$ , we study when the twisted group $C^{*}$ -algebra $C_{r}^{*} (G, σ)$ is selfless, in the sense of Robert. For a countably infinite a…

math.OA2026

The Bures metric and the quantum metric on the density space of a C*-algebra: the non-unital case

Konrad Aguilar, Karina Behera, Katrine von Bornemann Hjelmborg +4

Building off work of Farenick and Rahaman, we extend the definition of the density space and the Bures metric to the setting of non-unital C*-algebras equipped with a faithful trac…

math.OA2025

Metrics on completely positive maps via noncommutative geometry

Are Austad, Erik Bédos, Jonas Eidesen +2

We study methods of inducing metrics on unital completely positive maps by employing seminorms arising in noncommutative geometry. Our main approach relies on the development of an…

math.CO2024

New classes of reversible cellular automata

Jan Kristian Haugland, Tron Omland

A Boolean function $f$ on $k$ ~bits induces a shift-invariant vectorial Boolean function $F$ from $n$ bits to $n$ bits for every $n \geq k$ . If $F$ is bijective for every $n$ , we say…

math.CO2024

Shift-invariant transformations and almost liftings

Jan Kristian Haugland, Tron Omland

We investigate shift-invariant transformations, also known as rotation-symmetric vectorial Boolean functions, on $n$ bits that are induced from Boolean functions on $k$ bits, for $…

math.OA2024

On the Bures metric, C*-norm, and the quantum metric

Konrad Aguilar, Karina Behera, Tron Omland +1

We prove that the topology on the density space with respect to a unital C*-algebra and a faithful induced by the C*-norm is finer than the Bures metric topology. We also provide a…

math.OA2022

Strong Pedersen rigidity for coactions of compact groups

S. Kaliszewski, Tron Omland, John Quigg +1

We prove a version of Pedersen's outer conjugacy theorem for coactions of compact groups, which characterizes outer conjugate coactions of a compact group in terms of properties of…

math.OA2022★ 4 cited

C-irreducibility for reduced twisted group C-algebras

Erik Bédos, Tron Omland

We study C*-irreducibility of inclusions of reduced twisted group C*-algebras and of reduced group C*-algebras. We characterize C*-irreducibility in the case of an inclusion arisin…

math.CO2022★ 1 cited

Permutation rotation-symmetric S-boxes, liftings and affine equivalence

Tron Omland, Pantelimon Stanica

In this paper, we investigate permutation rotation-symmetric (shift-invariant) vectorial Boolean functions on $n$ bits that are liftings from Boolean functions on $k$ bits, for $k\…

math.FA2020

Deformations and Balian-Low theorems for Gabor frames on the adeles

Ulrik Enstad, Mads S. Jakobsen, Franz Luef +1

We generalize Feichtinger and Kaiblinger's theorem on linear deformations of uniform Gabor frames to the setting of a locally compact abelian group $G$ . More precisely, we show tha…

math.OA2018

Rigidity theory for $C^{*}$ -dynamical systems and the "Pedersen Rigidity Problem", II

S. Kaliszewski, Tron Omland, John Quigg

This is a follow-up to a paper with the same title and by the same authors. In that paper, all groups were assumed to be abelian, and we are now aiming to generalize the results to…

math.OA2018

C*-algebras of right LCM one-relator monoids and Artin-Tits monoids of finite type

Xin Li, Tron Omland, Jack Spielberg

We study C*-algebras generated by left regular representations of right LCM one-relator monoids and Artin-Tits monoids of finite type. We obtain structural results concerning nucle…

math.OA2018★ 2 cited

Free nilpotent groups are C*-superrigid

Tron Omland

The free nilpotent group $G_{m, n}$ of class $m$ and rank $n$ is the free object on $n$ generators in the category of nilpotent groups of class at most $m$ . We show that $G_{m, n}$ c…

math.OA2017★ 1 cited

C*-simplicity of HNN extensions and groups acting on trees

Rasmus Sylvester Bryder, Nikolay A. Ivanov, Tron Omland

We study non-ascending HNN extensions acting on their Bass-Serre trees, and characterize C*-simplicity and the unique trace property by means of the kernel and quasi-kernels of the…

math.OA2016

Rigidity theory for $C^{*}$ -dynamical systems and the "Pedersen Rigidity Problem"

S. Kaliszewski, Tron Omland, John Quigg

Let $G$ be a locally compact abelian group. By modifying a theorem of Pedersen, it follows that actions of $G$ on $C^{*}$ -algebras $A$ and $B$ are outer conjugate if and only if ther…

math.OA2016★ 1 cited

Dynamical systems and operator algebras associated to Artin's representation of braid groups

Tron Omland

Artin's representation is an injective homomorphism from the braid group $B_{n}$ on $n$ strands into $Aut F_{n}$ , the automorphism group of the free group $\math…

math.OA2016

On reduced twisted group C*-algebras that are simple and/or have a unique trace

Erik Bédos, Tron Omland

We study the problem of determining when the reduced twisted group C*-algebra associated with a discrete group G is simple and/or has a unique tracial state, and present new suffic…

math.OA2016★ 10 cited

C*-simplicity of free products with amalgamation and radical classes of groups

Nikolay A. Ivanov, Tron Omland

We give new characterizations to ensure that a free product of groups with amalgamation has a simple reduced group C*-algebra, and provide a concrete example of an amalgam with tri…

math.OA2015★ 21 cited

On the K-theory of C*-algebras arising from integral dynamics

Selçuk Barlak, Tron Omland, Nicolai Stammeier

We investigate the $K$ -theory of unital UCT Kirchberg algebras $Q_{S}$ arising from families $S$ of relatively prime numbers. It is shown that $K_{*} (Q_{S})$ is the d…

math.OA2015★ 3 cited

Dualities for maximal coactions

S. Kaliszewski, Tron Omland, John Quigg

We present a new construction of crossed-product duality for maximal coactions that uses Fischer's work on maximalizations. Given a group $G$ and a coaction $(A, δ)$ we define a gen…

math.OA2015

Destabilization

S. Kaliszewski, Tron Omland, John Quigg

This partly expository paper first supplies the details of a method of factoring a stable C*-algebra A as B \otimes K in a canonical way. Then it is shown that this method can be p…

math.OA2015

Three versions of categorical crossed-product duality

S. Kaliszewski, Tron Omland, John Quigg

In this partly expository paper we compare three different categories of C*-algebras in which crossed-product duality can be formulated, both for actions and for coactions of local…

Z-stable and selfless inclusions for the infinite braid group

Universal Quantum Computation with Multi-Mode Schrödinger Cat States Stabilized by Non-Local Dissipation Engineering

Selflessness for twisted group C*-algebras of amenable groups and their inclusions

The Bures metric and the quantum metric on the density space of a C*-algebra: the non-unital case

Metrics on completely positive maps via noncommutative geometry

New classes of reversible cellular automata

Shift-invariant transformations and almost liftings

On the Bures metric, C*-norm, and the quantum metric

Strong Pedersen rigidity for coactions of compact groups

C*-irreducibility for reduced twisted group C*-algebras

Permutation rotation-symmetric S-boxes, liftings and affine equivalence

Deformations and Balian-Low theorems for Gabor frames on the adeles

Rigidity theory for C∗-dynamical systems and the "Pedersen Rigidity Problem", II

C*-algebras of right LCM one-relator monoids and Artin-Tits monoids of finite type

Free nilpotent groups are C*-superrigid

C*-simplicity of HNN extensions and groups acting on trees

Rigidity theory for C∗-dynamical systems and the "Pedersen Rigidity Problem"

Dynamical systems and operator algebras associated to Artin's representation of braid groups

On reduced twisted group C*-algebras that are simple and/or have a unique trace

C*-simplicity of free products with amalgamation and radical classes of groups

On the K-theory of C*-algebras arising from integral dynamics

Dualities for maximal coactions

Destabilization

Three versions of categorical crossed-product duality

$Z$ -stable and selfless inclusions for the infinite braid group

C-irreducibility for reduced twisted group C-algebras

Rigidity theory for $C^{*}$ -dynamical systems and the "Pedersen Rigidity Problem", II

Rigidity theory for $C^{*}$ -dynamical systems and the "Pedersen Rigidity Problem"