# nLab matrix Lie algebra

Contents

### Context

#### $\infty$-Lie theory

Background

Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids

Cohomology

Homotopy

Related topics

Examples

$\infty$-Lie groupoids

$\infty$-Lie groups

$\infty$-Lie algebroids

$\infty$-Lie algebras

# Contents

## Definition

A matrix Lie algebra is the Lie algebra that is canonically a sub-Lie algebra of the general linear Lie algebra $Mat(n) = \mathfrak{gl}(n)$ of $n \times n$ matrices.