Journal of Operator Theory

Volume 44, Issue 1, Summer 2000 pp. 91-112.

On automorphisms of

$C^*$ -algebras associated with subshifts

Authors: Kengo Matsumoto
Author institution: Yokohama City University, 22--2 Seto, Kanazawa-ku, Yokohama, 236--0027, Japan

Summary: We prove that, for a given one-sided subshift

$X_\Lambda$ , any non-trivial automorphism of the subshift always yields an outer automorphism of the

$C^*$ -algebra

${\cal O}_{\Lambda}$ associated with the subshift. In particular, any non-trivial automorphism of the one-sided topological Markov shift

$X_A$ for a

$\{ 0,1\}$ -matrix

$A$ yields an outer automorphism of the Cuntz-Krieger algebra

${\cal O}_A$ . We also determine the form of the automorphisms of the

$C^*$ -algebra

${\cal O}_{\Lambda}$ arising from automorphisms of the subshift

$X_\Lambda$ .

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