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Stabilized $C^*$-algebras constructed from symbolic dynamical systems

Published online by Cambridge University Press:  01 June 2000

KENGO MATSUMOTO
Affiliation:
Department of Mathematics, Joetsu University of Education, Joetsu 943-8512, Japan (e-mail: matsu@juen.ac.jp)
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Abstract

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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 a separable Hilbert space and the $C^*$-algebras constructed from creation operators on sub-Fock spaces associated with the subshifts. We also prove that the gauge actions on the stabilized $C^*$-algebras are invariant for topological conjugacy as two-sided subshifts under some conditions. Hence, if two subshifts are topologically conjugate as two-sided subshifts, the associated stabilized $C^*$-algebras are isomorphic so that their K-groups are isomorphic.

Information

Type
Research Article
Copyright
2000 Cambridge University Press