Associative homotopy Lie algebras and Wronskians

We analyze representations of Schlessinger-Stasheff associative homotopy Lie algebras by higher-order differential operators. W-transformations of chiral embeddings of a complex curve related with the Toda equations into Kähler manifolds are shown to be endowed with the homotopy Lie-algebra structures. Extensions of the Wronskian determinants preserving Schlessinger-Stasheff algebras are constructed for the case of n ≥ 1 independent variables.