nLab
nilpotent L-infinity algebra

Contents

Context

\infty-Lie theory

∞-Lie theory (higher geometry)

Background

Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids

Cohomology

Homotopy

Examples

\infty-Lie groupoids

\infty-Lie groups

\infty-Lie algebroids

\infty-Lie algebras

Higher algebra

Rational homotopy theory

Contents

Idea

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

Under the formal duality between L L_\infty -algebras and their Chevalley-Eilenberg dgc-algebras, connective nilpotent L 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 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.