Universal enveloping algebra
= Universal enveloping algebra
{wiki=Universal_enveloping_algebra}
The universal enveloping algebra is a fundamental concept in the theory of Lie algebras and representation theory. Given a Lie algebra \\(\\mathfrak\{g\}\\), its universal enveloping algebra, denoted as \\(U(\\mathfrak\{g\})\\), is an associative algebra that encodes the structure of the Lie algebra in such a way that representation theory can be applied to it using methods of associative algebras.