Contents

# Contents

## Idea

The Lie algebra $\mathfrak{sl}(2,k)$ (over some ground field $k$) is the special linear Lie algebra $\mathfrak{sl}(n,k)$ for $n = 2$.

Over ground field $k = \mathbb{R}$ (real numbers) or $k = \mathbb{C}$ (complex numbers) this is the Lie algebra corresponding to the Lie group which is the special linear group $SL(2,\mathbb{R})$ or $SL(2,\mathbb{C})$, respectively.

## Properties

### As the complexification of $\mathfrak{su}(2)$

$\mathfrak{sl}(2,\mathbb{C})$ is the complexification of the special unitary Lie algebra $\mathfrak{su}(2)$ (see at su(2)) (…)

### Jacobson-Morozov theorem

See at Jacobson-Morozov theorem.

Created on December 4, 2019 at 09:26:51. See the history of this page for a list of all contributions to it.