On a multiparametric quantized enveloping algebra

Abstract

Let A = A(p, λ) be the multiparameter deformation of the coordinate algebra of n × n matrices as described by Artin, Schelter and TÄte. Let U be the quantum enveloping algebra which is associ-ated to A, in the sense of Fad dee v, Reshetikhin and Takhtadzhyan. When the parameter λ is not a root of unity, we classify the skew primitive elements of U and describe the group of Hopf algebra automorphisms of a subalgebra U ^′ of u. Finally, we find some of the central group-like elements of U.