Inductive Construction Of U_q (sl_n)

S.Majid can get a new Hopf algebra structure from a quasitriangular Hopf algebra H and any braided group in the category of H-modules,by the double bosonization theory.Moreover,He gets a new construction of Lusztig's quantization universal enveloping algebra Uq(g)and a higher rank one.Specially,when g=sln, this paper gives the specific process of from Uq(sln)to Uq(sln+1)by this theory, combining with right Uqext(sln)module Aq,which is a braided group generated by {ei|i=1,...,n).At last,giving briefly q-combination formula of{ei|i=1,...,n}, according to {Ei,Fi|i=1,...,n}which generate Uq(sln+1).