Journal article
Monic representations of finite higher-rank graphs
Ergodic theory and dynamical systems, Vol.40(5), pp.1238-1267
05/2020
DOI: 10.1017/etds.2018.79
Abstract
In this paper, we define the notion of monic representation for the $C^{\ast }$-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 $C^{\ast }$-algebra of the continuous functions on the infinite path space, admit a cyclic vector. We link monic representations to the $\unicode[STIX]{x1D6EC}$-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.
Details
- Title: Subtitle
- Monic representations of finite higher-rank graphs
- Creators
- CARLA Farsi - 1Department of Mathematics, University of Colorado at Boulder, Boulder, CO 80309-0395, USA email carla.farsi@colorado.edu, packer@euclid.colorado.eduELIZABETH Gillaspy - University of MontanaPALLE Jorgensen - 3Department of Mathematics, 14 MLH, University of Iowa, Iowa City, IA 52242-1419, USA email palle-jorgensen@uiowa.eduSOORAN Kang - Chung-Ang UniversityJUDITH Packer - 1Department of Mathematics, University of Colorado at Boulder, Boulder, CO 80309-0395, USA email carla.farsi@colorado.edu, packer@euclid.colorado.edu
- Resource Type
- Journal article
- Publication Details
- Ergodic theory and dynamical systems, Vol.40(5), pp.1238-1267
- DOI
- 10.1017/etds.2018.79
- ISSN
- 0143-3857
- eISSN
- 1469-4417
- Publisher
- Cambridge University Press
- Number of pages
- 30
- Language
- English
- Date published
- 05/2020
- Academic Unit
- Mathematics
- Record Identifier
- 9984241159002771
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