Oz's crib sheet: Lie theory
Edited by Toby Bartels

A Lie group G has a lie algebra g. If a is an element of g and A is defined to be exp a, then A is an element of G.



A Lie bracket [,] is defined on the lie algebra g and produces another element of the set g. For matrices, this is [a,b] = ab-ba.

Same examples:

Complete definitions:

Given a Lie group G, which specific Lie algebra g is the Lie algebra of the Lie group G?
The space tangent to the identity element 1 of G.

Go back to Oz's crib sheet.

This web page was written between 2000 and 2002 by Toby Bartels, Oz, and probably some other people, but I forget just who. Toby reserves no legal rights to it.

The permanent URI of this web page is http://tobybartels.name/Oz/Lie/.