  We show that except in several cases conjugacy classes of classical Weyl
groups $W(B_n)$ and $W(D_n)$ are of type {\rm D}. We prove that except in three
cases Nichols algebras of irreducible Yetter-Drinfeld ({\rm YD} in short
)modules over the classical Weyl groups are infinite dimensional. We establish
the relationship between Fomin-Kirillov algebra $\mathcal E_n$ and Nichols
algebra $\mathfrak{B} ({\mathcal O}_{{(1, 2)}} , \epsilon \otimes {\rm sgn})$
of transposition over symmetry group by means of quiver Hopf algebras. We
generalize {\rm FK } algebra. The characteristic of finiteness of Nichols
algebras in thirteen ways and of {\rm FK } algebras ${\mathcal E}_n$ in nine
ways is given. All irreducible representations of finite dimensional Nichols
algebras %({\rm FK } algebras ${\mathcal E}_n$) and a complete set of hard
super- letters of Nichols algebras of finite Cartan types are found. The
sufficient and necessary condition for Nichols algebra $\mathfrak B(M)$ of
reducible {\rm YD} module $M$ over $A \rtimes \mathbb{S}_n$ with ${\rm supp }
(M) \subseteq A$ to be finite dimensional is given. % Some conditions for a
braided vector space to become a {\rm YD} module over finite commutative group
are obtained. It is shown that hard braided Lie Lyndon word, standard Lyndon
word, Lyndon basis path, hard Lie Lyndon word and standard Lie Lyndon word are
the same with respect to $ \mathfrak B(V)$, Cartan matrix $A_c$ and $U(L^+)$,
respectively, where $V$ and $L$ correspond to the same finite Cartan matrix
$A_c$.
