universal enveloping algebra
A universal enveloping algebra of a Lie algebra over a field is an associative http://planetmath.org/node/Algebraalgebra (with unity) over , together with a Lie algebra homomorphism (where the Lie algebra structure on is given by the commutator), such that if is a another associative algebra over and is another Lie algebra homomorphism, then there exists a unique homomorphism of associative algebras such that the diagram