Multiparameter quantum enveloping algebras Original Research Article

Let A = A(p, λ) be the multiparameter deformation of the coordinate algebra of n × 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 λ is not a root of unity. Our approach depends on a cocycle twisting method which reduces many arguments to the standard one-parameter deformation.