nLab
derivation Lie 2-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

Contents

Definition

For 𝔤\mathfrak{g} a Lie algebra, its derivation Lie 2-algebra is the corresponding automorphism ∞-Lie algebra:

it is the strict Lie 2-algebra coming from the differential crossed module that is given by the chain complex

:𝔤AdDer(𝔤) \partial : \mathfrak{g} \stackrel{Ad}{\to} Der(\mathfrak{g})

equipped with the canonical Lie action? of the derivation Lie algebra? Der(𝔤)Der(\mathfrak{g}) on 𝔤\mathfrak{g}.

Created on August 28, 2011 13:23:15 by Urs Schreiber (89.204.153.64)