Double Yangian and the universal R-matrix

Abstract

We describe the double Yangian of the general linear Lie algebra gl N by following a general scheme of Drinfeld. We also describe the centre of the Yangian by using its Hopf algebra structure, and provide a proof of the analogue of the Poincaré—Birkhoff—Witt theorem for the Yangian based on its representation theory. This proof extends to the double Yangian.