The local integration of Leibniz algebras  [ L’intégration locale des algèbres de Leibniz ]
Annales de l'Institut Fourier, Tome 63 (2013) no. 1, pp. 1-35.

Cet article apporte une solution locale au problème des coquecigrues pour les algèbres de Leibniz. Ce problème consiste à trouver une généralisation de la structure de groupe (de Lie) dont les algèbres de Leibniz sont les structures tangentes associées. En utilisant les liens entre cohomologie d’algèbre de Leibniz et cohomologie de rack de Lie, nous généralisons l’intégration d’une algèbre de Lie en un groupe de Lie en prouvant que toute algèbre de Leibniz est isomorphe à l’algèbre de Leibniz tangente d’un rack de Lie local. Cet article se termine avec l’exemple de l’intégration d’une algèbre de Leibniz de dimension 5.

This article gives a local answer to the coquecigrue problem for Leibniz algebras, that is, the problem of finding a generalization of the (Lie) group structure such that Leibniz algebras are the corresponding tangent algebra structure. Using links between Leibniz algebra cohomology and Lie rack cohomology, we generalize the integration of a Lie algebra into a Lie group by proving that every Leibniz algebra is isomorphic to the tangent Leibniz algebra of a local Lie rack. This article ends with an example of a Leibniz algebra integration in dimension 5.

DOI : https://doi.org/10.5802/aif.2754
Classification : 17A32,  20M99
Mots clés : Algèbre de Leibniz, rack de Lie, cohomologie d’algèbre de Leibniz, cohomologie de rack.
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     author = {Covez, Simon},
     title = {The local integration of Leibniz algebras},
     journal = {Annales de l'Institut Fourier},
     pages = {1--35},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {63},
     number = {1},
     year = {2013},
     doi = {10.5802/aif.2754},
     mrnumber = {3089194},
     zbl = {06177075},
     language = {en},
     url = {www.numdam.org/item/AIF_2013__63_1_1_0/}
}
Covez, Simon. The local integration of Leibniz algebras. Annales de l'Institut Fourier, Tome 63 (2013) no. 1, pp. 1-35. doi : 10.5802/aif.2754. http://www.numdam.org/item/AIF_2013__63_1_1_0/

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