Lie element

Given a Lie algebra $\mathfrak{g}$ and its univeral enveloping algebra $\mathfrak{U(g)}$ , then an element $x\in\mathfrak{U(g)}$ is called a Lie element if $x$ is in the image of $\mathfrak{g}$ in $\mathfrak{U(g)}$ .

This term is most often used for free Lie algebras and specifically in the famous Baker-Campbell-Hausdorff formula (theorem).

Title	Lie element
Canonical name	LieElement
Date of creation	2013-03-22 16:51:14
Last modified on	2013-03-22 16:51:14
Owner	Algeboy (12884)
Last modified by	Algeboy (12884)
Numerical id	4
Author	Algeboy (12884)
Entry type	Definition
Classification	msc 17B35
Classification	msc 16S30
Defines	Lie element