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2008 Operad of formal homogeneous spaces and Bernoulli numbers
Sergei Merkulov
Algebra Number Theory 2(4): 407-433 (2008). DOI: 10.2140/ant.2008.2.407


It is shown that for any morphism, ϕ:gh, 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.


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Sergei Merkulov. "Operad of formal homogeneous spaces and Bernoulli numbers." Algebra Number Theory 2 (4) 407 - 433, 2008.


Received: 10 October 2007; Revised: 17 January 2008; Accepted: 9 March 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1162.18003
MathSciNet: MR2411406
Digital Object Identifier: 10.2140/ant.2008.2.407

Primary: 18D50
Secondary: 11B68 , 55P48

Keywords: Bernoulli number , Lie algebra , operad

Rights: Copyright © 2008 Mathematical Sciences Publishers


Vol.2 • No. 4 • 2008
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