Lie algebra

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, 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.


tidy | en | sembr

Footnotes

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