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

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

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

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English
Article number	67
Journal	Integral Equations and Operator Theory
Volume	90
Issue number	6
DOIs	https://doi.org/10.1007/s00020-018-2493-z
State	Published - Dec 1 2018

Funding

E.G. was partially supported by the Deutsches Forschungsgemeinschaft via the SFB 878 “Groups, Geometry, and Actions” of the Westfälische-Wilhelms-Universität Münster. S.K. was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (# NRF-2017R1D1A1B03034697). C.F. and J.P. were partially supported by two individual grants from the Simons Foundation (C.F. #523991; J.P. #316981). E.G. was partially supported by the Deutsches Forschungsgemeinschaft via the SFB 878 “Groups, Geometry, and Actions” of the Westfälische-Wilhelms-Universität Münster. S.K. was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (# NRF-2017R1D1A1B03034697). C.F. and J.P. were partially supported by two individual grants from the Simons Foundation (C.F. #523991; J.P. #316981).

Funders	Funder number
1800749
Simons Foundation	523991, 316981
SFB 878
Ministry of Education	NRF-2017R1D1A1B03034697
2017R1D1A1B03034697

Keywords

Higher-rank graphs
Irreducible representations
Permutative representations
Projection-valued measure
Purely atomic representations

Access to Document

10.1007/s00020-018-2493-z

Cite this

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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.",

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AU - Gillaspy, Elizabeth

AU - Jorgensen, Palle

AU - Kang, Sooran

AU - Packer, Judith

PY - 2018/12/1

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KW - Higher-rank graphs

KW - Irreducible representations

KW - Permutative representations

KW - Projection-valued measure

KW - Purely atomic representations

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