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

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

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

Mathematical Sciences

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

5 Scopus citations

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.

Original language	English
Pages (from-to)	766-798
Number of pages	33
Journal	Journal of Mathematical Analysis and Applications
Volume	468
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2018.08.051
State	Published - Dec 15 2018

Funding

C.F. also thanks IMPAN for hospitality during her visits to IMPAN, Warsaw, Poland, where some of this work was carried out (grant #3542/H2020/2016/2). This paper was partially supported by the grant H2020-MSCA-RISE-2015-691246-QUANTUM DYNAMICS. C.F. also thanks IMPAN for hospitality during her visits to IMPAN, Warsaw, Poland, where some of this work was carried out (grant # 3542/H2020/2016/2 ). This paper was partially supported by the grant H2020-MSCA-RISE-2015-691246-QUANTUM DYNAMICS. The authors would like to thank Alex Kumjian and Daniel Gonçalves for helpful discussions. E.G. was partially supported by the Deutsches Forschungsgemeinshaft via the SFB 878 “Groups, Geometry, and Actions” of the 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 ). P.J. thanks his colleagues in the Math Department at the University of Colorado, for making a week-long visit there possible, for support, and for kind hospitality.

Funders	Funder number
Simons Foundation	523991, 316981
691246
NRF-2017R1D1A1B03034697
SFB 878

Keywords

C-algebras
Markov measures
Perron–Frobenius
Representations
k-graphs
Λ-semibranching function systems

Access to Document

10.1016/j.jmaa.2018.08.051

Cite this

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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.",

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