  We establish the relationship among Nichols algebras, Nichols braided Lie
algebras and Nichols Lie algebras. We prove two results: (i) Nichols algebra
$\mathfrak B(V)$ is finite-dimensional if and only if Nichols braided Lie
algebra $\mathfrak L(V)$ is finite-dimensional if there does not exist any
$m$-infinity element in $\mathfrak B(V)$; (ii) Nichols Lie algebra $\mathfrak
L^-(V)$ is infinite dimensional if $ D^-$ is infinite. We give the sufficient
conditions for Nichols braided Lie algebra $\mathfrak L(V)$ to be a homomorphic
image of a braided Lie algebra generated by $V$ with defining relations.

Quantum Algebra