Monic representations of finite higher-rank graphs

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

doi:10.1017/etds.2018.79

Monic representations of finite higher-rank graphs

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

Mathematical Sciences

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

8 Scopus citations

Abstract

In this paper, we define the notion of monic representation for the-algebras of finite higher-rank graphs with no sources, and we undertake a comprehensive study of them. Monic representations are the representations that, when restricted to the commutative-algebra of the continuous functions on the infinite path space, admit a cyclic vector. We link monic representations to the-semibranching representations previously studied by Farsi, Gillaspy, Kang and Packer (Separable representations, KMS states, and wavelets for higher-rank graphs. J. Math. Anal. Appl. 434 (2015), 241-270) and also provide a universal representation model for non-negative monic representations.

Original language	English
Pages (from-to)	1238-1267
Number of pages	30
Journal	Ergodic Theory and Dynamical Systems
Volume	40
Issue number	5
DOIs	https://doi.org/10.1017/etds.2018.79
State	Published - May 1 2020

Funding

Acknowledgements. The authors would like to thank Daniel Gonc¸alves, Janos Englander and Alex Kumjian for helpful discussions. E.G. was partially supported by the Deutsches Forschungsgemeinschaft 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 (#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. Progress towards the completion of this manuscript was made by the first three named co-authors while in attendance at the Fields Institute (Toronto) and the Mathematical Congress of the Americas (Montreal) in 2017; we are grateful for their support of our collaboration. 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.

Funders	Funder number
SFB 878
Ministry of Education	2017R1D1A1B03034697
Simons Foundation	523991, 316981
691246

Keywords

3-semibranching function systems
Markov measures
monic representations
projective systems

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10.1017/etds.2018.79

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Monic representations of finite higher-rank graphs

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