∞-Lie theory

# Contents

## Definition

For $\mathfrak{g}$ 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

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

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

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