Definition:Lie Group

Definition

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

Also see

• Results about Lie groups can be found here.

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
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Lie, Marius Sophus (1842-99)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Lie, Marius Sophus (1842-99)