We introduce super Yangians of $\mathfrak{gl}(V),\mathfrak{sl}(V)$ (in the new Drinfeld realization) associated to all Dynkin diagrams of $\mathfrak{gl}(V)$, where $V$ is a finite-dimensional super vector space. We show that all of them are isomorphic to the super Yangians introduced by Maxim Nazarov, by identifying them with the corresponding RTT super Yangians. However, their "positive halves" are not pairwise isomorphic, and we obtain the shuffle algebra realizations of those. We adapt the latter to the trigonometric setup by obtaining the shuffle algebra realizations of the "positive halves" of type $A$ quantum loop superalgebras associated to arbitrary Dynkin diagrams.

中文翻译：

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所有嘉当数据的 A 型超级杨氏和量子仿射超代数的混洗代数实现

我们引入了与 $\mathfrak{gl}(V)$ 的所有 Dynkin 图相关联的 $\mathfrak{gl}(V),\mathfrak{sl}(V)$（在新的 Drinfeld 实现中）的超级 Yangians，其中 $ V$ 是一个有限维的超向量空间。我们通过将它们与相应的 RTT 超级 Yangians 识别，表明它们都与 Maxim Nazarov 引入的超级 Yangians 同构。然而，它们的“正半部分”不是成对同构的，我们获得了它们的混洗代数实现。我们通过获得与任意 Dynkin 图相关联的 $A$ 类型量子环超代数的“正半部分”的混洗代数实现，使后者适应三角学设置。