  Let $V$ be a braided vector space of diagonal type. Let $\mathfrak B(V)$,
$\mathfrak L^-(V)$ and $\mathfrak L(V)$ be the Nichols algebra, Nichols Lie
algebra and Nichols braided Lie algebra over $V$, respectively. We show that a
monomial belongs to $\mathfrak L(V)$ if and only if that this monomial is
connected. We obtain the basis for $\mathfrak L(V)$ of arithmetic root systems
and the dimension for $\mathfrak L(V)$ of finite Cartan type. We give the
sufficient and necessary conditions for $\mathfrak B(V) = F\oplus \mathfrak
L^-(V)$ and $\mathfrak L^-(V)= \mathfrak L(V)$. We obtain an explicit basis of
$\mathfrak L^ - (V)$ over quantum linear space $V$ with $\dim V=2$.
