Lie theory for nilpotent L∞-algebras

  title={Lie theory for nilpotent L∞-algebras},
  author={Ezra Getzler},
  journal={Annals of Mathematics},
  • E. Getzler
  • Published 1 April 2004
  • Mathematics
  • Annals of Mathematics
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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