On Pointed Hopf Algebra With Weyl Groups Of Exceptional Type

All-1-type pointed Hopf algebras with Weyl groups of exceptional type are found.It is proved that every non-1-type pointed Hopf algebra is infinite dimensional. We get two important results as follows:Let G be a Weyl group of Exceptional type.Then(â…°)For any bi-one Nichols algebra B(O_s,x)over Weyl group G,there exist s_i in the first column of Table of G and j with 1≤j≤v_i¹such that B(O_s,x)≌B(O_si,x_i^j)is a graded pull-push YD Hopf algebra isomorphism;(â…±)B(O_si,x_i^j)is of-1-type if and only if j appears in fourth column of Table of G;(â…²)dim(B(O_si,x_i^j)=∞if j does not appears in fourth column of Table of G.Let H be a pointed Hopf algebra with Weyl group G=G(H)of exceptional type.Then(â…°)There exists an RSR(G,r,(?),u)such that(?)≌B(G,r,(?),u)is graded pull-push YD Hopf algebra isomorphism,where R:=diag_filt(H)and(?)is the subalgebra generated by R₁as algebras in R;for any C∈K_r(G)and p∈I_C(r,u), there exists s_i in the first column in Tables of G and 1≤j≤v_i¹such that u(C)=s_i and x_C^p=x_i^j.Let A_G:={i| there exists C∈K_r(G)such that s_i∈C} and for any i∈A_G,B_i,G:= {j| there exists p∈I_C(r,u)such that x_Osi^P=x_i^j}.(â…±)H is of-1-type if and only if for any i∈A_G and any j∈B_i,G,j appears in the fourth column of Table of G.(â…²)If there exist i∈A_G and j∈B_i,Gsuch that j does not appear in the fourth column of Table G,then dimH=∞.