nLab
Lie operad

Context

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

Higher algebra

Contents

Idea

Given an ambient additive symmetric monoidal category, the Lie operad is the operad whose algebras over an operad are Lie algebras in that category. It is a quadratic operad? whose Koszul dual is the operad for commutative algebras.

In the case of the monoidal category of chain complexes, we also say dg-Lie-operad. Its cofibrant resolution in the model structure on operads is the L-infinity operad whose algebras over an operad are L-∞-algebras.

References

Revised on August 13, 2012 10:37:52 by Beren Sanders (96.251.14.54)