We establish the relationship among Nichols algebras, Nichols braided Lie
algebras and Nichols Lie algebras. We prove two results: (i) Nichols algebra
B(V) is finite-dimensional if and only if Nichols braided Lie
algebra L(V) is finite-dimensional if there does not exist any
m-infinity element in B(V); (ii) Nichols Lie algebra Lβ(V) is infinite dimensional if Dβ is infinite. We give the sufficient
conditions for Nichols braided Lie algebra L(V) to be a homomorphic
image of a braided Lie algebra generated by V with defining relations.Comment: LeTex 18 pages, need JOLT-macros to compile. To appear in Journal of
Lie Theor