Centre of a Lie algebra

The centre of a Lie algebra is a Lie algebra ideal consisting of elements which annihilate all elements in the Lie bracket, #m/def/lie i.e.

It is the kernel of the adjoint Lie algebra representation and thus an ideal of .¹

Properties

Any linear subspace of is an ideal of , called a Central ideal.

#state/tidy | #lang/en | #SemBr

It is otherwise easy to convince oneself that this is an ideal, since it “absorbs” all elements by sending them to zero. ↩