Operad of formal homogeneous spaces and Bernoulli numbers

It is shown that for any morphism, phi : g -> h, of Lie algebras the vector space underlying the Lie algebra h is canonically a g-homogeneous formal manifold with the action of g being highly nonlinear and twisted by Bernoulli numbers. This fact is obtained from a study of the 2-coloured operad of formal homogeneous spaces whose minimal resolution gives a new conceptual explanation of both Ziv Ran's Jacobi-Bernoulli complex and Fiorenza-Manetti's L-infinity-algebra structure on the mapping cone of a morphism of two Lie algebras. All these constructions are iteratively extended to the case of a morphism of arbitrary L-infinity-algebras.