Lie algebra Lie algebra ideal A Lie algebra ideal is just an algebra ideal of a Lie algebra. lie Equivalently, is a submodule under the adjoint representation. Note that a Lie subalgebra is a (two-sided) ideal iff it is a left or right ideal, by the alternating property. A Lie algebra is simple iff it has no nontrivial ideals. Properties Let be ideals. Then is an ideal is an ideal is an ideal (see Commutator ideal) Proof ^P1 and ^P2 follow immediately. Note that for any , by ^P1 so is an ideal. Special ideals Centre of a Lie algebra Kernel of a Lie algebra homomorphism Central ideal Radical of a Lie algebra See also Quotient Lie algebra tidy | en | sembr