TY - JOUR
T1 - Monic representations of finite higher-rank graphs
AU - Farsi, Carla
AU - Gillaspy, Elizabeth
AU - Jorgensen, Palle
AU - Kang, Sooran
AU - Packer, Judith
N1 - Publisher Copyright:
© Cambridge University Press, 2018.
PY - 2020/5/1
Y1 - 2020/5/1
N2 - 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.
AB - 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.
KW - 3-semibranching function systems
KW - Markov measures
KW - monic representations
KW - projective systems
UR - http://www.scopus.com/inward/record.url?scp=85053137349&partnerID=8YFLogxK
U2 - 10.1017/etds.2018.79
DO - 10.1017/etds.2018.79
M3 - Article
AN - SCOPUS:85053137349
SN - 0143-3857
VL - 40
SP - 1238
EP - 1267
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 5
ER -