**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 [1] and studied in the papers [2, 3] sequel to [1]. 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 ([5], [6]) 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.