nLab
primitive element

An element $x\in C$ in a coalgebra (or, more generally coring) $(C,\Delta ,ϵ)$ is primitive if $\Delta (x)=1\otimes x+x\otimes 1$ and $ϵ(x)=0$. By Milnor-Moore theorem, for Hopf algebras over a field of characteristics zero, the subspace of primitive elements generates a subalgebra which is isomorphic to the enveloping algebra of some Lie algebra.