C*-algebras of labelled graphs

Abstract

We describe a class of $C^{\ast }$-algebras which simultaneously generalise the ultragraph algebras of Tomforde and the shift space $C^{\ast }$-algebras of Matsumoto. In doing so we shed some new light on the different $C^{\ast }$-algebras that may be associated to a shift space. Finally, we show how to associate a simple $C^{\ast }$-algebra to an irreducible sofic shift.

References in corpus (3)

• A unified approach to Exel-Laca algebras and C*-algebras associated to graphs
• On C*-algebras Associated with Sofic Shifts
• Symbolic Dynamics, Partial Dynamical Systems, Boolean Algebras and C*-algebras Generated by Partial Isometries

Cited by in corpus (18)

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• Gauge-invariant ideals of C*-algebras of Boolean dynamical systems
• $C^{\ast }$-algebras associated with textile dynamical systems
• A Generalised uniqueness theorem and the graded ideal structure of Steinberg algebras
• The structure of gauge-invariant ideals of labelled graph $C^{\ast }$-algebras
• C*-algebras of separated graphs
• On Flow Equivalence of Sofic Shifts
• Topological freeness for $C^{\ast }$-correspondences
• On simple labelled graph $C^{\ast }$-algebras
• Primitive Ideals of Labelled Graph $C^{\ast }$-algebras
• The socle of subshift algebras, with applications to subshift conjugacy
• C*-algebras associated with Hilbert C*-quad modules of C*-textile dynamical systems
• $C^{\ast }$-algebras associated to $C^{\ast }$-correspondences and applications to mirror quantum spheres
• Pushdown automata, lambda-graph systems and C*-algebras
• A Cuntz--Krieger uniqueness theorem for semigraph $C^{\ast }$-algebras
• On freely generated semigraph $C^{\ast }$-algebras
• C*-algebras of labelled graphs II - Simplicity results