Let A be a prime ∗-algebra and preserve ∗-Lie n-tuple derivations on A, that is, for every A1, A2, . . . , An ∈ A, (A1 A2 · · · An) = (A1) A2 · · · An + A1 (A2) · · · An + · · ·+ A1 A2 · · · (An) where Ai Aj = Ai Aj − Aj A∗ i for i , j ∈ N, then is additive. Moreover, if (i I2 ) is self-adjoint then is a ∗-derivation. The result is also valid when A is a von Neumann algebra without central abelian projections.
