Double Yangian and the universal $R$-matrix

Maxim Nazarov

Abstract: We describe the double Yangian of the general linear Lie algebra $\mathfrak{gl}_N$ 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.