21 citations · 47 across the 23 of their papers we have counts for
24 papers · 1 filter
Rapidly growing AF algebras
Konrad Aguilar, Stephan Ramon Garcia, Evelyne Knight +2
We introduce certain families of AF algebras associated to Bratteli diagrams arising from numerical semigroup theory, a branch of combinatorics. Curry-Schoenberg B-splines, staples…
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…
Spectral Triples on a non-standard presentation of Effros-Shen AF algebras
Konrad Aguilar, Samantha Brooker, Jack Spielberg
The Effros-Shen algebra corresponding to an irrational number can be described by an inductive sequence of direct sums of matrix algebras, where the continued fraction expansio…
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…
Domains of quantum metrics on AF algebras
Konrad Aguilar, Katrine von Bornemann Hjelmborg, Frederic Latremoliere
Given a compact quantum metric space (A, L), we prove that the domain of L coincides with A if and only if A is finite dimensional. We then show how one can explicitly build many q…
Quantum Gromov-Hausdorff propinquity convergence of Christensen-Ivan quantum metrics on AF algebras
Clay Adams, Konrad Aguilar, Esteban Ayala +2
We provide convergence in the quantum Gromov-Hausdorff propinquity of Latrémolière of some sequences of infinite-dimensional Leibniz compact quantum metric spaces of Rieffel given…
The Hamming Distance and the Fell Topology on AF Algebras
Konrad Aguilar, Zoë X. Batterman
We introduce a new metric on the ideal space of an AF algebra that metrizes the Fell topology. The novelty of this metric lies in the use of a Hamming distance type metric in its c…
The strongly Leibniz property and the Gromov--Hausdorff propinquity
Konrad Aguilar, Stephan Ramon Garcia, Elena Kim +1
We construct a new version of the dual Gromov--Hausdorff propinquity that is sensitive to the strongly Leibniz property. In particular, this new distance is complete on the class o…
The Fell topology and the modular Gromov-Hausdorff propinquity
Konrad Aguilar, Jiahui Yu
Given a unital AF-algebra equipped with a faithful tracial state, we equip each (norm-closed two-sided) ideal of with a metrized quantum vector bundle structure, when canon…
Frobenius-Rieffel norms on finite-dimensional C*-algebras
Konrad Aguilar, Stephan Ramon Garcia, Elena Kim
In 2014, Rieffel introduced norms on certain unital C*-algebras built from conditional expectations onto unital C*-subalgebras. We begin by showing that these norms generalize the…
Compact Quantum Metric Spaces from Free Graph Algebras
Konrad Aguilar, Michael Hartglass, David Penneys
Starting with a vertex-weighted pointed graph , we form the free loop algebra defined in Hartglass-Penneys' article on canonical -algebras assoc…
Polynomial approximation of quantum Lipschitz functions
Konrad Aguilar, Jens Kaad, David Kyed
We prove an approximation result for Lipschitz functions on the quantum sphere , from which we deduce that the two natural quantum metric structures on have quantum…
The Podles spheres converge to the sphere
Konrad Aguilar, Jens Kaad, David Kyed
We prove that the Podles spheres converge in quantum Gromov-Hausdorff distance to the classical 2-sphere as the deformation parameter tends to 1. Moreover, we construct…
Bunce-Deddens algebras as quantum Gromov-Hausorff distance limits of circle algebras
Konrad Aguilar, Frederic Latremoliere, Timothy Rainone
We show that Bunce-Deddens algebras, which are AT-algebras, are also limits of circle algebras for Rieffel's quantum Gromov-Hausdorff distance, and moreover, form a continuous fami…
A quantum metric on the Cantor Space
Konrad Aguilar, Alejandra López
The first author and Latrémolière had introduced a quantum metric (in the sense of Rieffel) on the algebra of complex-valued continuous functions on the Cantor space. We show that…
Quantum metrics on the tensor product of a commutative C*-algebra and an AF C*-algebra
Konrad Aguilar
Given a compact metric space X and a unital AF algebra A equipped with a faithful tracial state, we place quantum metrics on the tensor product of C(X) and A given established quan…
Quantum metrics from the trace on full matrix algebras
Konrad Aguilar, Samantha Brooker
We prove that, in the sense of the Gromov-Hausdorff propinquity, certain natural quantum metrics on the algebras of -matrices are separated by a positive distance when n…
Inductive limits of C*-algebras and compact quantum metrics spaces
Konrad Aguilar
Given a unital inductive limit of C*-algebras for which each C*-algebra of the inductive sequence comes equipped with a compact quantum metric of Rieffel, we produce sufficient con…
The Podles sphere as a spectral metric space
Konrad Aguilar, Jens Kaad
We study the spectral metric aspects of the standard Podles sphere, which is a homogeneous space for quantum SU(2). The point of departure is the real equivariant spectral triple i…
Standard homogeneous C*-algebras as compact quantum metric spaces
Konrad Aguilar, Tristan Bice
Given a compact metric space X and a unital C*-algebra A, we introduce a family of seminorms on the C*-algebra of continuous functions from X to A, denoted C(X, A), induced by clas…
Some applications of conditional expectations to convergence for the quantum Gromov-Hausdorff propinquity
Konrad Aguilar, Frederic Latremoliere
We prove that all the compact metric spaces are in the closure of the class of full matrix algebras for the quantum Gromov-Hausdorff propinquity. We also show that given an action…
AF algebras in the quantum Gromov-Hausdorff propinquity space
Konrad Aguilar
For unital AF algebras with faithful tracial states, we provide criteria for convergence in the quantum Gromov-Hausdorff propinquity. For any unital AF algebra, we introduce new Le…
Convergence of Quotients of AF Algebras in Quantum Propinquity by Convergence of Ideals
Konrad Aguilar
We introduce a topology on the ideal space of inductive limits of C*-algebras built by a topological inverse limit of the Fell topologies on the C*-algebras of the given inductive…
Quantum Ultrametrics on AF Algebras and The Gromov-Hausdorff Propinquity
Konrad Aguilar, Frederic Latremoliere
We construct quantum metric structures on unital AF algebras with a faithful tracial state, and prove that for such metrics, AF algebras are limits of their defining inductive sequ…