# 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 LieElement 2013-03-22 16:51:14 2013-03-22 16:51:14 Algeboy (12884) Algeboy (12884) 4 Algeboy (12884) Definition msc 17B35 msc 16S30 Lie element