Lie Algebra

A Lie Algebra is a Vector Space with an operation, a Lie Bracket, that satisfies the Jacobi Identity.

Jacobi Identity

A set A with two binary operations + and × , with an additive identity 0 will satisfy the Jacobi Identity if for all x, y, z in A, the following is true:

x×(y×z) + y×(z×x) + z×(x×y)=0

Lie Bracket

One example of a Lie Bracket operation is the cross product:

[x,y] = x × y

x=(x_1, x_2, x_3)

y=(y_1, y_2, y_3)