Sooran Kang

activity

20092022

most citedThe primitive ideals of the Cuntz-Krieger algebra of a row-finite higher-rank graph with no sources

46 citations · 71 across the 19 of their papers we have counts for

collaborators

22 papers

math.OA2022

Yang-Mills connections and sigma-models on quantum Heisenberg manifolds

Stine Marie Berge, Sooran Kang, Franz Luef

We construct a spectral triple on a quantum Heisenberg manifold, which generalizes the results of Chakraborty and Shinha, and associate to it an energy functional on the set of pro…

math.FA2019

An Infinite Dimensional Analysis of Kernel Principal Components

Palle E. T. Jorgensen, Sooran Kang, Myung-Sin Song +1

We study non-linear data-dimension reduction. We are motivated by the classical linear framework of Principal Component Analysis. In nonlinear case, we introduce instead a new kern…

math.OA2018

Yang-Mills connections on quantum Heisenberg manifolds

Sooran Kang, Franz Luef, Judith A. Packer

We investigate critical points and minimizers of the Yang-Mills functional YM on quantum Heisenberg manifolds $D_{μν}^{c}$ , where the Yang-Mills functional is defined on the set of a…

math.PR2018

Dirichlet forms and ultrametric Cantor sets associated to higher-rank graphs

Jaeseong Heo, Sooran Kang, Yongdo Lim

The aim of this paper is to study the heat kernel and jump kernel of the Dirichlet form associated to ultrametric Cantor sets $\partial\BB_Λ$ that is the infinite path space of the…

math.OA2018★ 3 cited

Purely atomic representations of higher-rank graph C*-algebras

Carla Farsi, Elizabeth Gillaspy, Palle Jorgensen +2

We study purely atomic representations of C*-algebras associated to row-finite and source-free higher-rank graphs. We describe when purely atomic representations are unitarily equi…

math.OA2018

Spectral triples for higher-rank graph $C^{*}$ -algebras

Carla Farsi, Elizabeth Gillaspy, Antoine Julien +2

In this note, we present a new way to associate a spectral triple to the noncommutative $C^{*}$ -algebra $C^{*} (Λ)$ of a strongly connected finite higher-rank graph $Λ$ . We generalize a…

math.OA2018★ 6 cited

Monic representations of finite higher-rank graphs

Carla Farsi, Elizabeth Gillaspy, Palle Jorgensen +2

In this paper we define the notion of monic representation for the $C^{*}$ -algebras of finite higher-rank graphs with no sources, and undertake a comprehensive study of them. Monic r…

math.OA2018

Representations of higher-rank graph $C^{*}$ -algebras associated to $Λ$ -semibranching function systems

Carla Farsi, Elizabeth Gillaspy, Palle E. T. Jorgensen +2

In this paper, we discuss a method of constructing separable representations of the $C^{*}$ -algebras associated to strongly connected row-finite $k$ -graphs $Λ$ . We begin by giving an…

math.OA2018

Spectral triples and wavelets for higher-rank graphs

Carla Farsi, Elizabeth Gillaspy, Antoine Julien +2

In this paper, we present a new way to associate a finitely summable spectral triple to a higher-rank graph $Λ$ , via the infinite path space $Λ^{\infty}$ of $Λ$ . Moreover, we prove t…

math.OA2017★ 2 cited

Separable representations of higher-rank graphs

Carla Farsi, Elizabeth Gillaspy, Palle Jorgensen +2

In this monograph we undertake a comprehensive study of separable representations (as well as their unitary equivalence classes) of $C^{*}$ -algebras associated to strongly connected…

math.OA2017★ 5 cited

Wavelets and spectral triples for higher-rank graphs

Carla Farsi, Elizabeth Gillaspy, Antoine Julien +2

In this paper, we present two new ways to associate a spectral triple to a higher-rank graph $Λ$ . Moreover, we prove that these spectral triples are intimately connected to the wav…

math.OA2016

KMS states on the operator algebras of reducible higher-rank graphs

Astrid an Huef, Sooran Kang, Iain Raeburn

We study the equilibrium or KMS states of the Toeplitz C*-algebra of a finite higher-rank graph which is reducible. The Toeplitz algebra carries a gauge action of a higher-dimensio…

math.OA2016

Wavelets and spectral triples for fractal representations of Cuntz algebras

Carla Farsi, Elizabeth Gillaspy, Antoine Julien +2

In this article we provide an identification between the wavelet decompositions of certain fractal representations of $C^{*} -$ algebras of directed graphs of M. Marcolli and A. Paoluc…

math.OA2016

Wavelets and graph $C^{*}$ -algebras

Carla Farsi, Elizabeth Gillaspy, Sooran Kang +1

Here we give an overview on the connection between wavelet theory and representation theory for graph $C^{*}$ -algebras, including the higher-rank graph $C^{*}$ -algebras of A. Kumj…

math.OA2015

Separable representations, KMS states, and wavelets for higher-rank graphs

Carla Farsi, Elizabeth Gillaspy, Sooran Kang +1

Let $Λ$ be a strongly connected, finite higher-rank graph. In this paper, we construct representations of $C^{*} (Λ)$ on certain separable Hilbert spaces of the form $L^{2} (X, μ)$ , by in…

math.OA2014★ 2 cited

Spatial realisations of KMS states on the C*-algebras of higher-rank graphs

Astrid an Huef, Sooran Kang, Iain Raeburn

Several authors have recently been studying the equilibrium or KMS states on the Toeplitz algebras of finite higher-rank graphs. For graphs of rank one (that is, for ordinary direc…

math.OA2014★ 1 cited

Quantum Heisenberg Manifolds as Twisted Groupoid $C^{*}$ -Algebras

Sooran Kang, Alex Kumjian, Judith Packer

The quantum Heisenberg manifolds are noncommutive manifolds constructed by M. Rieffel as strict deformation quantizations of Heisenberg manifolds and have been studied by various a…

math.DS2013

Computing the fundamental group of a higher-rank graph

Sooran Kang, David Pask, Samuel B. G. Webster

We compute a presentation of the fundamental group of a higher-rank graph using a coloured graph description of higher-rank graphs developed by the third author. We compute the fun…

math.OA2013★ 46 cited

The primitive ideals of the Cuntz-Krieger algebra of a row-finite higher-rank graph with no sources

Toke Meier Carlsen, Sooran Kang, Jacob Shotwell +1

We catalogue the primitive ideals of the Cuntz-Krieger algebra of a row-finite higher-rank graph with no sources. Each maximal tail in the vertex set has an abelian periodicity gro…

math.OA2011

Co-universal C*-algebras associated to aperiodic k-graphs

Sooran Kang, Aidan Sims

We construct a representation of each finitely aligned aperiodic k-graph Λ on the Hilbert space H^{ap} with basis indexed by aperiodic boundary paths in Λ. We show that the canonic…

math.OA2011★ 6 cited

Aperiodicity and the primitive ideal space of a row-finite $k$ -graph $C^{*}$ -algebra

Sooran Kang, David Pask

We describe the primitive ideal space of the $C^{*}$ -algebra of a row-finite $k$ -graph with no sources when every ideal is gauge invariant. We characterize which spectral spaces…

math.OA2009

The Yang-Mills functional and Laplace's equation on quantum Heisenberg manifolds

Sooran Kang

In this paper, we discuss the Yang-Mills functional and a certain family of its critical points on quantum Heisenberg manifolds using noncommutative geometrical methods developed b…

Yang-Mills connections and sigma-models on quantum Heisenberg manifolds

An Infinite Dimensional Analysis of Kernel Principal Components

Yang-Mills connections on quantum Heisenberg manifolds

Dirichlet forms and ultrametric Cantor sets associated to higher-rank graphs

Purely atomic representations of higher-rank graph C*-algebras

Spectral triples for higher-rank graph C∗-algebras

Monic representations of finite higher-rank graphs

Representations of higher-rank graph C∗-algebras associated to Λ-semibranching function systems

Spectral triples and wavelets for higher-rank graphs

Separable representations of higher-rank graphs

Wavelets and spectral triples for higher-rank graphs

KMS states on the operator algebras of reducible higher-rank graphs

Wavelets and spectral triples for fractal representations of Cuntz algebras

Wavelets and graph C∗-algebras

Separable representations, KMS states, and wavelets for higher-rank graphs

Spatial realisations of KMS states on the C*-algebras of higher-rank graphs

Quantum Heisenberg Manifolds as Twisted Groupoid C∗-Algebras

Computing the fundamental group of a higher-rank graph

The primitive ideals of the Cuntz-Krieger algebra of a row-finite higher-rank graph with no sources

Co-universal C*-algebras associated to aperiodic k-graphs

Aperiodicity and the primitive ideal space of a row-finite k-graph C∗-algebra

The Yang-Mills functional and Laplace's equation on quantum Heisenberg manifolds

Spectral triples for higher-rank graph $C^{*}$ -algebras

Representations of higher-rank graph $C^{*}$ -algebras associated to $Λ$ -semibranching function systems

Wavelets and graph $C^{*}$ -algebras

Quantum Heisenberg Manifolds as Twisted Groupoid $C^{*}$ -Algebras

Aperiodicity and the primitive ideal space of a row-finite $k$ -graph $C^{*}$ -algebra