W algebras are L∞ algebras

A bstract It is shown that the closure of the infinitesimal symmetry transformations underlying classical W algebras give rise to L ∞ algebras with in general field dependent gauge parameters. Therefore, the class of well understood W algebras provides highly nontrivial examples of such strong homotopy Lie algebras. We develop the general formalism for this correspondence and apply it explicitly to the classical W 3 algebra.