nLab
Lie 3-algebra

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

Contemts

Definition

A Lie 3-algebra or 33-Lie algebra is a 3-truncated L-∞-algebra. Under Lie integration is the infinitesimal approximation to a Lie 3-group.

Models by 2-crossed modules

A semistrict model for Lie 3-algebras, analogous to that of 3-groupoids that are Gray groupoids is given by differential 2-crossed modules.

Examples

References

Lie 3-algebras coming from differential 2-crossed modules and parallel transport for Lie 3-algebra valued forms is discussed in

Revised on December 7, 2016 04:35:44 by Urs Schreiber (217.155.201.6)