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

Carla Farsi; Elizabeth Gillaspy; Palle Jorgensen; Sooran Kang; Judith Packer

doi:10.1016/j.jmaa.2018.08.051

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

Journal article

Peer reviewed

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

Carla Farsi, Elizabeth Gillaspy, Palle Jorgensen, Sooran Kang and Judith Packer

Journal of mathematical analysis and applications, Vol.468(2), pp.766-798

12/15/2018

DOI: 10.1016/j.jmaa.2018.08.051

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Abstract

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 alternative characterization of the Λ-semibranching function systems introduced in an earlier paper, with an eye towards constructing such representations that are faithful. Our new characterization allows us to more easily check that examples satisfy certain necessary and sufficient conditions. We present a variety of new examples relying on this characterization. We then use some of these methods and a direct limit procedure to identify a faithful separable representation for any row-finite source-free k-graph.

Markov measures

[formula omitted]-algebras

k-graphs

Perron–Frobenius

Representations

Λ-semibranching function systems

Details

Title: Subtitle: Representations of higher-rank graph C⁎-algebras associated to Λ-semibranching function systems
Creators: Carla Farsi - Department of Mathematics, University of Colorado at Boulder, Boulder, CO 80309-0395, USA
Elizabeth Gillaspy - Department of Mathematics, University of Montana, 32 Campus Drive #0864, Missoula, MT 59812-0864, USA
Palle Jorgensen - Department of Mathematics, 14 MLH, University of Iowa, Iowa City, IA 52242-1419, USA
Sooran Kang - College of General Education, Chung-Ang University, 84 Heukseok-ro, Dongjak-gu, Seoul, Republic of Korea
Judith Packer - Department of Mathematics, University of Colorado at Boulder, Boulder, CO 80309-0395, USA
Resource Type: Journal article
Publication Details: Journal of mathematical analysis and applications, Vol.468(2), pp.766-798
DOI: 10.1016/j.jmaa.2018.08.051
ISSN: 0022-247X
eISSN: 1096-0813
Publisher: Elsevier Inc
Grant note: DOI: 10.13039/501100004869, name: Universität Münster, award: SFB 878; DOI: 10.13039/501100003725, name: National Research Foundation of Korea, award: NRF-2017R1D1A1B03034697; DOI: 10.13039/100000893, name: Simons Foundation, award: 523991, 316981; DOI: 10.13039/501100014433, name: IMPAN, award: 3542/H2020/2016/2
Language: English
Date published: 12/15/2018
Academic Unit: Mathematics
Record Identifier: 9983985883502771

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