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.

中文翻译：

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双重Yangian和通用R矩阵

我们通过遵循Drinfeld的一般方案来描述一般线性Lie代数gl _N的双Yangian 。我们还使用其Hopf代数结构描述了洋基的中心，并基于其表示理论为洋基的庞加莱-伯克霍夫-维特定理提供了类似的证明。这种证明延伸到双重仰光。