2007/05/23 by Kengo Matsumoto, Matsumoto, Kengo
Mathematics · #46L05.} #46L35 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Secondary 37B10
paper · pdf · doi:10.48550/arxiv.0705.3283
openalex publication_date 2007/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.