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Monic representations of finite higher-rank graphs
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 40 / Issue 5 / May 2020
- Published online by Cambridge University Press:
- 06 September 2018, pp. 1238-1267
- Print publication:
- May 2020
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- Article
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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.
