Drinfel'd–Jimbo coproduct of quantized GIM Lie algebras

We define a sequence of quotient algebras of a quantized GIM Lie algebra's tensor algebras, modulo ideals generated by some imaginary root vectors, so that there are algebra morphisms similar to the Drinfel'd–Jimbo coproduct of quantum groups, and hence the quantized GIM Lie algebra has properties which are similar to those of Hopf algebras. Weight modules and quantum loop modules of the corresponding quantum affine Kac–Moody algebra are used to construct tensor modules of the quantized GIM Lie algebra via the coproduct.