Lie Algebra

This is n×n complex matrices.

[A,B]=AB-BA

Lie Algebra is the standard commutator on M.

T-commutator is nonzero matrix.

A,B∈M

[A,A]T=0

This is a bilinear map.

M^T

M^1=M

It satisfies Jacobi identity.

When T is invertible, M is isomorphic.

ad-bc≠0

When T isn't invertible, M isn't isomorphic.

Moreover, M^T and M^S are Lie isomorphic, if T and S aren't invertible, although T and S are the same rank.

When T is all trace, [A,B]T=0