We prove that the Yangian associated to an untwisted symmetric affine Kac–Moody Lie algebra is isomorphic to the Drinfeld double of a shuffle algebra. The latter is constructed in [YZ14] as an algebraic formalism of cohomological Hall algebras. As a consequence, we obtain the Poincare–Birkhoff–Witt (PBW) theorem for this class of affine Yangians. Another independent proof of the PBW theorem is given recently by Guay, Regelskis, and Wendlandt [GRW18].

中文翻译：

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仿射仰光的PBW定理

我们证明，与未扭转的对称仿射Kac-Moody Lie代数相关的Yangian与shuffle代数的Drinfeld双态同构。后者在[YZ14]中作为同调霍尔代数的代数形式主义构造。结果，我们得到了此类仿射洋人的庞加莱—伯克霍夫—威特（PBW）定理。Guay，Regelskis和Wendlandt [GRW18]最近又给出了PBW定理的另一个独立证明。