Algebra & Number Theory
- Algebra Number Theory
- Volume 2, Number 4 (2008), 407-433.
Operad of formal homogeneous spaces and Bernoulli numbers
It is shown that for any morphism, , of Lie algebras the vector space underlying the Lie algebra is canonically a -homogeneous formal manifold with the action of 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 -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 -algebras.
Algebra Number Theory, Volume 2, Number 4 (2008), 407-433.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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