Actions of symbolic dynamical systems on $C^{\ast }$-algebras II. Simplicity of $C^{\ast }$-symbolic crossed products and some examples

Abstract

We have introduced a notion of $C^{\ast }$-symbolic dynamical system in [K. Matsumoto: Actions of symbolic dynamical systems on $C^{\ast }$-algebras, to appear in J. Reine Angew. Math.], that is a finite family of endomorphisms of a $C^{\ast }$-algebra with some conditions. The endomorphisms are indexed by symbols and yield both a subshift and a $C^{\ast }$-algebra of a Hilbert $C^{\ast }$-bimodule. The associated $C^{\ast }$-algebra with the $C^{\ast }$-symbolic dynamical system is regarded as a crossed product by the subshift. We will study a simplicity condition of the $C^{\ast }$-algebras of the $C^{\ast }$-symbolic dynamical systems. Some examples such as irrational rotation Cuntz-Krieger algebras will be studied.

28 pages

References in corpus (1)

• A construction of $C^{\ast }$-algebras from $C^{\ast }$-correspondences