Actions of symbolic dynamical systems on $C^*$-algebras II. Simplicity of $C^*$-symbolic crossed products and some examples

Details Actions of symbolic dynamical systems on $C^*$-algebras II. Simplicity of $C^*$-symbolic crossed products and some examples Actions of symbolic dynamical systems on $C^*$-algebras II. Simplicity of $C^*$-symbolic crossed products and some examples

2007-05-23

arxiv.org/abs/0705.3283v1

Mathematics

Operator Algebras

28 pages

Scientific paper

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

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