The local integration of Leibniz algebras

@article{Covez2010TheLI,
  title={The local integration of Leibniz algebras},
  author={Simon Covez},
  journal={arXiv: Rings and Algebras},
  year={2010}
}
  • Simon Covez
  • Published 18 November 2010
  • Mathematics
  • arXiv: Rings and Algebras
This article gives a local answer to the coquecigrue problem. Hereby we mean the problem, formulated by J-L. Loday in \cite{LodayEns}, is that of finding a generalization of the Lie's third theorem for Leibniz algebra. That is, we search a manifold provided with an algebraic structure which generalizes the structure of a (local) Lie group, and such that the tangent space at a distinguished point is a Leibniz algebra structure. Moreover, when the Leibniz algebra is a Lie algebra, we want that… 
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In this note we point out that the definition of the universal enveloping dialgebra for a Leibniz algebra is consistent with the interpretation of a Leibniz algebra as a generalization not of a Lie
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Kupershmidt operator is a key to extend a Leibniz algebra by its representation. In this paper, we investigate several structures related to Kupershmidt operators on Leibniz algebras and introduce
Itô’s theorem and metabelian Leibniz algebras
We prove that the celebrated Itô’s theorem for groups remains valid at the level of Leibniz algebras: if is a Leibniz algebra such that , for two abelian subalgebras and , then is metabelian, i.e. .
Enhanced Leibniz Algebras: Structure Theorem and Induced Lie 2-Algebra
An enhanced Leibniz algebra is an algebraic struture that arises in the context of particular higher gauge theories describing self-interacting gerbes. It consists of a Leibniz algebra $$({\mathbb
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The "coquecigrue" problem for Leibniz algebras is that of finding an appropriate generalization of Lie's third theorem, that is, of finding a generalization of the notion of group such that Leibniz
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