# Lie theory for nilpotent L∞-algebras

@article{Getzler2004LieTF, title={Lie theory for nilpotent L∞-algebras}, author={Ezra Getzler}, journal={Annals of Mathematics}, year={2004}, volume={170}, pages={271-301} }

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 γ from L ∞ -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…

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