Free Lie algebra
= Free Lie algebra
{title2=$\mathcal L_R(X)$}
The <Lie algebra> over a commutative ring $R$ generated by a set $X$ subject only to bilinearity, alternation and the <Jacobi identity>. Every map from $X$ to the underlying set of an $R$-<Lie algebra> extends uniquely to a <Lie algebra homomorphism>. It can be constructed from bracketed words by quotienting by those identities; elements are represented by <Lie polynomials>.