nLab
primitive element

An element xCx\in C in a coalgebra (or, more generally coring) (C,Δ,ϵ)(C,\Delta,\epsilon) is primitive if Δ(x)=1x+x1\Delta(x) = 1\otimes x + x\otimes 1 and ϵ(x)=0\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)