# Definition:Lie Group

Jump to navigation
Jump to search

## Definition

A **Lie group** is a group which is also a smooth manifold.

## Source of Name

This entry was named for Marius Sophus Lie.

## Historical Note

When the concept of a Lie group was originally researched, it did not appear to have any immediate practical application.

In more recently times, they have been used:

- to describe pseudo-Riemannian locally homogeneous symmetric spaces, to be used in geometric theory of gravitation
- to model phenomena in quantum mechanics, from $1925$ to $1926$, via Hermitian matrix representations of observations

## Sources

- 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {B}.26$: Extensions of the Complex Number System. Algebras, Quaternions, and Lagrange's Four Squares Theorem