nLab primitive element

Context

Algebra

higher algebra

universal algebra

Theorems

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