$C^{\ast }$-algebras associated to Boolean dynamical systems

Abstract

The goal of these notes is to present the C*-algebra $C^{\ast }(B,L,\theta )$ of a Boolean dynamical system $(B,L,\theta )$, that generalizes the $C^{\ast }$-algebra associated to Labelled graphs introduced by Bates and Pask, and to determine its simplicity, its gauge invariant ideals, as well as compute its K-Theory

References in corpus (4)

• C*-algebras of labelled graphs
• Symbolic Dynamics, Partial Dynamical Systems, Boolean Algebras and C*-algebras Generated by Partial Isometries
• The structure of gauge-invariant ideals of labelled graph $C^{\ast }$-algebras
• On simple labelled graph $C^{\ast }$-algebras

Cited by in corpus (8)

• Diagonal-preserving graded isomorphisms of Steinberg algebras
• Gauge-invariant ideals of C*-algebras of Boolean dynamical systems
• A Generalised uniqueness theorem and the graded ideal structure of Steinberg algebras
• Condition (K) for Boolean dynamical systems
• C*-algebras of Boolean inverse monoids - traces and invariant means
• Purely infinite labeled graph $C^{\ast }$-algebras
• AF-embeddable labeled graph $C^{\ast }$-algebras
• The simplicity of the C*-algebras associated to arbitrary labeled spaces