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We show that except in several cases conjugacy classes of classical Weylgroups $W(B_n)$ and $W(D_n)$ are of type {\rm D}. We prove that except in threecases Nichols algebras of irreducible Yetter-Drinfeld ({\rm YD} in short)modules over the classical Weyl groups are infinite dimensional.

Nichols algebras over classical Weyl groups