# 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 $X_\Lambda$.

**Keywords:**$C^*$-algebras, automorphisms, subshifts, Cuntz-Krieger algebras

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