# nLab nilpotent L-infinity algebra

Contents

## Examples

### $\infty$-Lie algebras

#### Higher algebra

higher algebra

universal algebra

and

# Contents

## 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

Last revised on July 22, 2021 at 13:46:15. See the history of this page for a list of all contributions to it.