Operad of formal homogeneous spaces and Bernoulli numbers

Details Operad of formal homogeneous spaces and Bernoulli numbers Operad of formal homogeneous spaces and Bernoulli numbers

2007-08-07

arxiv.org/abs/0708.0891v2

Algebra & Number Theory, Vol. 2 (2008), No. 4, 407-433.

Mathematics

Quantum Algebra

LaTeX, 18 pages. minor changes; the final journal version

Scientific paper

It is shown that for any morphism, i: 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 the study of a 2-coloured operad of formal homogeneous spaces and its minimal resolution, and is used to give 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.

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