Nichols Algebras Of Reducible YD Module Over Weyl Groups Of Exceptional Type

It is proved that except a few cases Nichols algebras of reducible Yetter-Drinfeldmodules over Weyl groups of exceptional type are infinite dimensional.Through the research of Nichols Algebras of reducible Yetter-Drinfeld module overexceptional type Weyl groups E₆, E₇, E₈, F₄, G₂, we determine the dimension of itsNichols algebras whether the dimension is finite. We have removed a lot of cases withinfinite dimension. This is important for further study, and we get one important resultas follows:Let G be a Weyl group of exceptional type. Then dim(B(M(O_si,ρ¹)⊕M(O_sj,ρ²))=∞in the following cases:(i)G = W(E₆) .(ii) G = W(E₇) and (i,j) = (9,11), (9,13), (11,19), (13,19) and i,j = 6.(iii) G = W(E₈) and (i,j) = (8,14), (8,24), (14,35), (14,80), (24,35), (24,80)and i,j = 7.(iv) G = W(F₄) and (i,j) = (3,3), (3,4), (3,7), (3,8), (3,17), (3,18), (3,24),(3,25), (4,4), (4,7), (4,8), (4,17), (4,18), (4,24), (4,25), (7,13), (7,17), (7,18), (8,13),(8,17), (8,18), (13,17), (13,18) and i,j = 2.(v) G = W(G₂) and (i,j) = (2,5), (3,5), (5,5) and i,j = 4.