MULTIPARAMETER QUANTUM ENVELOPING-ALGEBRAS

Let A = A(p, lambda) be the multiparameter deformation of the coordina te algebra of n x n matrices as described by Artin, et al. (1991). Let U be the quantum enveloping algebra which is associated to A, in the sense of Faddeev, Reshetikhin and Takhtadzhyan. We prove a PBW theorem for U and establish a presentation by generators and relations, when lambda is not a root of unity. Our approach depends on a cocycle twist ing method which reduces many arguments to the standard one-parameter deformation.