RELATING THE APPROACHES TO QUANTIZED ALGEBRAS AND QUANTUM GROUPS

This paper constructs two representations of the quantum group Uqg' by exploiting its quotient structure and the quantum double construction. Here the quantum group is taken as the dual to the quantised algebra Uqg, a one parameter deformation of the universal enveloping algebra of the Lie algebra g, as in Drinfel'd [6] and Jimbo [10]. From the two representations, the Hopf structure of the quantised algebra Uqg is reexpressed in a matrix format. This is the very structure given by Faddeev et al. [7], in their approach to defining quantum groups and quantised algebras via the quantisation of the function space of the associated Lie group to g. © 1990 Springer-Verlag.