Algebra & Number Theory

Operad of formal homogeneous spaces and Bernoulli numbers

Sergei Merkulov

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Abstract

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.

Article information

Source
Algebra Number Theory, Volume 2, Number 4 (2008), 407-433.

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

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513797268

Digital Object Identifier
doi:10.2140/ant.2008.2.407

Mathematical Reviews number (MathSciNet)
MR2411406

Zentralblatt MATH identifier
1162.18003

Subjects
Primary: 18D50: Operads [See also 55P48]
Secondary: 11B68: Bernoulli and Euler numbers and polynomials 55P48: Loop space machines, operads [See also 18D50]

Keywords
operad Lie algebra Bernoulli number

Citation

Merkulov, Sergei. Operad of formal homogeneous spaces and Bernoulli numbers. Algebra Number Theory 2 (2008), no. 4, 407--433. doi:10.2140/ant.2008.2.407. https://projecteuclid.org/euclid.ant/1513797268


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