# nLab special linear Lie algebra

Contents

### Context

#### 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

## Idea,

For $k$ a field and $n$ a natural number, the special linear Lie algebra $\mathfrak{sl}(n,k)$ is the Lie algebra of trace-free $n\times n$-matrices with entries in $k$, with Lie bracket being the commutator of matrix multiplication.

## Examples

Last revised on June 9, 2022 at 19:48:39. See the history of this page for a list of all contributions to it.