nLab nilpotent L-infinity algebra

Idea

The generalization of the concept of nilpotent Lie algebra from Lie algebras to $L_\infty$-algebras..

Under the formal duality between $L_\infty$-algebras and their Chevalley-Eilenberg dgc-algebras, connective nilpotent $L_\infty$-algebras correspond bijectively to the connected Sullivan models (Berglund 2015, Thm. 2.3).

Properties

Rational homotopy theory

The fundamental theorem of dgc-algebraic rational homotopy theory says that the homotopy theory of nilpotent $L_\infty$-algebras of finite type over the rational numbers is equivalently that of rational nilpotent topological spaces of finite type.

References

• Ezra Getzler, Def. 4.2 in: Lie theory for nilpotent $L_\infty$ algebras, Annals of Mathematics, 170 (2009), 271–301 (math.AT/0404003)

• Alexander Berglund, Def. 2.1 in: Rational homotopy theory of mapping spaces via Lie theory for $L_\infty$ algebras, Homology, Homotopy and Applications, Volume 17 (2015) Number 2 (arXiv:1110.6145, doi:10.4310/HHA.2015.v17.n2.a16)