Abstract
We define a strong homotopy derivation of (cohomological) degree k of a strong homotopy algebra over an operad. This involves resolving the operad obtained from by adding a generator with "derivation relations".
For a wide class of Koszul operads , in particular and , we describe the strong homotopy derivations by coderivations and show that they are closed under the Lie bracket. We show that symmetrization of a strong homotopy derivation of an algebra yields a strong homotopy derivation of the symmetrized algebra.
We give examples of strong homotopy derivations generalizing inner derivations.