Purely Atomic Representations of Higher-Rank Graph C∗ -Algebras

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

doi:10.1007/s00020-018-2493-z

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Purely Atomic Representations of Higher-Rank Graph C∗ -Algebras

Journal article

Peer reviewed

Purely Atomic Representations of Higher-Rank Graph C∗ -Algebras

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

Integral equations and operator theory, Vol.90(6), pp.1-26

2018

DOI: 10.1007/s00020-018-2493-z

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Abstract

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 equivalent and we give necessary and sufficient conditions for a purely atomic representation to be irreducible in terms of the associated projection valued measures. We also investigate the relationship between purely atomic representations, monic representations and permutative representations, and we describe when a purely atomic representation admits a decomposition consisting of permutative representations.

Details

Title: Subtitle: Purely Atomic Representations of Higher-Rank Graph C∗ -Algebras
Creators: Carla Farsi
Elizabeth Gillaspy
Palle Jorgensen
Sooran Kang
Judith Packer
Resource Type: Journal article
Publication Details: Integral equations and operator theory, Vol.90(6), pp.1-26
DOI: 10.1007/s00020-018-2493-z
ISSN: 0378-620X
eISSN: 1420-8989
Grant note: DOI: 10.13039/501100003725, name: National Research Foundation of Korea, award: 2017R1D1A1B03034697; DOI: 10.13039/100000893, name: Simons Foundation, award: 523991, 316981; name: Deutsches Forschungsgemeinschaft, award: SFB 878
Language: English
Date published: 2018
Academic Unit: Mathematics
Record Identifier: 9983985807702771

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