The ideal structure of labeled graph C*-algebras
Associated to labeled graphs (E, L) a class of C*-algebras C*(E, L), called labeled graph C*-algebras, was introduced by Bates and Pask in  and studied in the papers [2, 3] sequel to . A C*-algebra in this class is defined to be a C*-algebra generated by a universal family of partial isometries satisfying certain relations determined by the labeled graph in question. By the universal property, a labeled graph C*-algebra always carries a gauge action of the unit cicle.
We will discuss the gauge-invariant ideal structure of labeled graph C*-algebras
based on the joint works (, ) with S. H. Kim and G. Park.
- T. Bates and D. Pask: C*-algebras of labelled graph, J. Operator Theory, 57:1 (2007), 207-226.
- T. Bates and D. Pask: C*-algebras of labelled graph II – Simplicity Results, Math. Scand., 104 (2009), 249-274.
- T. Bates, T. M. Carlsen, and D. Pask: C*-algebras of labelled graph III – K-theory computations,
Ergod. Th. \& Dynam. Sys., 37 (2017), 337–368.
- J. A Jeong, S. H. Kim and G. H. Park: The structure of gauge-invariant ideals of labelled graph C*-algebras, J. Funct. Anal., 262 (2012), 1759-1780.
- J. A Jeong and G. H. Park: Simple labeled graph C*-algebras are associated to disagreeable labeled spaces, J. Math. Anal. App., 461 (2018), 1391-1403.