We prove that the quantum toroidal algebras ${\mathcal{E}}_{\mathbf{s}}$ associated with different root systems s of ${\mathfrak{gl}}_{m|n}$ type are isomorphic. We also show the existence of Miki automorphism of ${\mathcal{E}}_{\mathbf{s}}$, which exchanges the vertical and horizontal subalgebras.

To obtain these results, we establish an action of the toroidal braid group on the direct sum ${\oplus }_{\mathbf{s}}{\mathcal{E}}_{\mathbf{s}}$ of all such algebras.

中文翻译：

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量子环形超代数上的辫子作用

我们证明了量子环形代数 ${\mathcal{乙}}_{\mathbf{秒}}$用不同的根系统相关联的小号的${\mathfrak{高尔}}_{米|n}$类型是同构的。我们还证明了 Miki 自同构的存在${\mathcal{乙}}_{\mathbf{秒}}$，交换垂直和水平子代数。

为了获得这些结果，我们建立了环形编织组对直接和的作用 ${\oplus }_{\mathbf{秒}}{\mathcal{乙}}_{\mathbf{秒}}$ 所有这些代数。