Majid conjecture: quantum Kac-Moody algebras version

Based on the n-fold tensor product version of the generalized double-bosonization construction, we prove the Majid conjecture of the quantum Kac-Moody algebras version. Particularly, we give explicitly the double-bosonization type-crossing constructions of quantum Kac-Moody algebras for affine types G2(1), E6(1), and T_p,q,r, and in this way, we can recover generators of quantum Kac-Moody algebras with braided groups defined by R-matrices in the related braided tensor category. This gives us a better understanding for the algebra structures themselves of the quantum Kac-Moody algebras as a certain extension of module-algebras/module-coalgebras with respect to the related quantum subalgebras of finite types inside.