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Outer Automorphisms on Cuntz Algebras

Authors:	Matsumoto, Kengo Tomiyama, Jun

Affiliation:	Department of Mathematics, Tokyo Metropolitan University Minami-Ohsawa 1-1, Hachioji-shi, Tokyo 192-03, Japan

Abstract:	We prove that if an automorphism ${alpha}$ on the Cuntz algebra O_n satisfies ${alpha}$ (S₁) = ${iota}$ S₁ for one isometry S₁ of generators S₁, ..., S_n suchthat , , l $≤$ i $≤$ n and a complex number ${lambda}$ with modulus one,then it is outer. In particular, any non trivial automorphismon O_n leaving one generator fixed is outer.

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