# nLab primitive element

### Context

#### Algebra

higher algebra

universal algebra

## Theorems

An element $x\in C$ in a coalgebra (or, more generally coring) $(C,\Delta,\epsilon)$ is primitive if $\Delta(x) = 1\otimes x + x\otimes 1$ and $\epsilon(x) = 0$. 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.

Revised on February 7, 2013 13:37:52 by Ingo Blechschmidt (137.250.162.16)