In mathematics, an Engel subalgebra of a Lie algebra with respect to some element x is the subalgebra of elements annihilated by some power of ad x. Engel subalgebras are named after Friedrich Engel. For finite-dimensional Lie algebras over infinite fields the minimal Engel subalgebras are the Cartan subalgebras.
See also Engel's theorem
References Winter, David J. (1972), Abstract Lie algebras, The M.I.T. Press, Cambridge, Mass.-London, ISBN 978-0-486-46282-0, MR 0332905