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.

Therefore:

Examples:

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:

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

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