Abstract

It is shown that for any morphism, φ : 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_∞-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_∞-algebras.

Keywords

operad, Lie algebra, Bernoulli number

Mathematical Subject Classification

Primary: 18D50

Secondary: 11B68, 55P48

Authors