THE THEOREM OF LIE AND HYPERPLANE SUBALGEBRAS OF LIE-ALGEBRAS

First is presented a proof of Lie's theorem on solvable Lie algebras based on the non-existence of the Heisenberg commutation relation. This is used to construct an effective procedure for finding all quotients of a given Lie algebra g which are isomorphic to the non-abelian two-dimensional algebra. As a byproduct one gets that the ideal DELTA(g) recently introduced by K. H. Hofmann is characteristic if the characteristic of the ground field is zero.