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Stabilized \(C^*\)-algebras constructed from symbolic dynamical systems. (English) Zbl 0964.46035

The following is a shortened version of author’s abstract: We construct stabilized \(C^*\)-algebras from subshifts by using the dynamical property of the symbolic dynamical systems. We prove that the construction is dynamical and the \(C^*\)-algebras are isomorphic to the tensor product \(C^*\)-algebras between the algebra of all compact operators on Hilbert space and the \(C^*\)-algebras constructed from creation operators on sub-Fock spaces associated with the subshifts.

MSC:

46L05 General theory of \(C^*\)-algebras
37B10 Symbolic dynamics
46L55 Noncommutative dynamical systems
37A55 Dynamical systems and the theory of \(C^*\)-algebras
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