Geodesic
Lie theory for nilpotent $L_\infty$-algebras
Ezra Getzler1
1 Department of Mathematics<br/>Northwestern University<br/>2033 Sheridan Road<br/>Evanston, IL 60208-2730<br/>United States
Annals of mathematics, Tome 170 (2009) no. 1, pp. 271-301.

Voir la notice de l'article provenant de la source Annals of Mathematics website

The Deligne groupoid is a functor from nilpotent differential graded Lie algebras concentrated in positive degrees to groupoids; in the special case of Lie algebras over a field of characteristic zero, it gives the associated simply connected Lie group. We generalize the Deligne groupoid to a functor $\gamma$ from $L_\infty$-algebras concentrated in degree $>-n$ to $n$-groupoids. (We actually construct the nerve of the $n$-groupoid, which is an enriched Kan complex.) The construction of gamma is quite explicit (it is based on Dupont’s proof of the de Rham theorem) and yields higher dimensional analogues of holonomy and of the Campbell-Hausdorff formula.
DOI : 10.4007/annals.2009.170.271

Ezra Getzler 1

1 Department of Mathematics<br/>Northwestern University<br/>2033 Sheridan Road<br/>Evanston, IL 60208-2730<br/>United States 
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Ezra Getzler. Lie theory for nilpotent $L_\infty$-algebras. Annals of mathematics, Tome 170 (2009) no. 1, pp. 271-301. doi : 10.4007/annals.2009.170.271. http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.170.271/

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