nLab
Lie 3-algebra

Context

\infty-Lie theory

∞-Lie theory

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

Created on July 22, 2010 15:47:39 by Urs Schreiber (87.212.203.135)