universal enveloping algebra
A universal enveloping algebra of a Lie algebra over
a field is an associative http://planetmath.org/node/Algebra
algebra (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