Lie algebras MOC Centralizer in a Lie algebra Let be a Lie algebra over and be a vector subspace. The centralizer of in is then the Lie subalgebra of elements giving zero bracket with all elements of , lie i.e. Proof of Lie subalgebra Let . By the ^Jacobi whence . A related notion is the Centre of a Lie algebra , which includes only those elements that give zero bracket for all elements. A weakening is the Normalizer in a Lie algebra. tidy | en | sembr