OUTER AUTOMORPHISMS ON CUNTZ ALGEBRAS

We prove that if an automorphism alpha on the Cuntz algebra O(n) satisfies alpha(S1) = lambdaS1 for one isometry S1 of generators S1,...,S(n) such that SIGMA(i=1)n S(i) S(i)* = 1, S(i)* S(i) = 1, 1 less-than-or-equal-to i less-than-or-equal-to n and a complex number lambda with modulus one, then it is outer* In particular, any non trivial automorphism on O(n) leaving one generator fixed is outer.