Kengo Matsumoto
Actions of symbolic dynamical systems on C*-algebras
We introduce a notion of C*-symbolic dynamical system, that is a finite family of endomorphisms of a C*-algebra with some conditions. The endomorphisms are indexed by symbols and yield both a nontrivial subshift and a Hilbert C*-bimodule. The associated C*-algebra with the Hilbert C*-bimodule is regarded as a crossed product by the subshift. We also introduce a notion of strong shift equivalence of C*-symbolic dynamical systems. We then prove that if two C*-symbolic dynamical systems are strong shift equivalent, the gauge actions of the crossed product C*-algebras by their subshifts are stably outer conjugate.
Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter
Print ISSN: 0075-4102
Volume: 2007, 04/2007
Pages: 23 - 49
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