THE TWO PARAMETER QUANTUM GROUPS U R, S (G) ASSOCIATED TO GENERALIZED KAC-MOODY ALGEBRA AND THEIR EQUITABLE PRESENTATION

We construct a family of two parameter quantum grou- ps Ur;s(g) associated with a generalized Kac-Moody algebra corre- sponding to symmetrizable admissible Borcherds Cartan matrix. We also construct the A-form UA and the classical limit of Ur;s(g). Furthermore, we display the equitable presentation for a subalgebra U b r;s (g) of Ur;s(g) and show that this presentation has the attractive feature that all of its generators act semisimply on nite dimen- sional irreducible Ur;s(g)-modules associated with the Kac-Moody algebra.