Let A be a simple unital AT algebra of real rank zero such that it has a unique tracial state { and K 1 (A) is neither 0 nor Z. For each . # Hom(K 1 (A), R) with dense range in R we construct a closed derivation $ in A which generates a oneparameter automorphism group : of A such that {($(u) u*)=2?i. ([u]) for any unitary u # D($). Furthermore we construct such an : with the Rohlin property, which is defined in Kishimoto (Comm. Math. Phys. 179 (1996), 599 622), in this case the crossed product A _ : R is a simple AT algebra of real rank zero. As an application we obtain that for such a C*-algebra A the kernel of the natural homomorphism of the group Inn(A) of approximately inner automorphisms into
is the group HInn(A) of automorphisms homotopic to inner automorphisms. Combining with the result of Kishimoto and Kumjian (Trans. Amer. Math. Soc., to appear), Inn(A)ΓHInn(A) is isomorphic to the above direct sum. As another application of the construction of derivations, we show that if A is a C*-algebra of the above type and : # HInn(A) has the Rohlin property and comes from . # Hom(K 1 (A), R) with dense range as in Kishimoto and Kumjian (preprint), then the crossed product A _ : Z is again of the same type; in particular A _ : Z is an AT algebra. (The other properties are known from Kishimoto [J. Operator Theory 40 (1998)].)