We revisit the free field construction of the deformed W-superalgebras ${\mathcal{W}}_{q,t}(\mathfrak{s}\mathfrak{l}(2|1))$ by Ding and Feigin, Contemp. Math. 248, 83–108 (1998), where the basic W-current and screening currents have been found. In this paper, we introduce higher W-currents and obtain a closed set of quadratic relations among them. These relations are independent of the choice of Dynkin diagrams for the superalgebra $\mathfrak{s}\mathfrak{l}(2|1)$, although the screening currents are not. This allows us to define ${\mathcal{W}}_{q,t}(\mathfrak{s}\mathfrak{l}(2|1))$ by generators and relations.

中文翻译：

---

变形W-超代数的二次关系Wq,t(sl(2|1))

我们重新审视变形的W -超代数的自由场构造${\mathcal{宽}}_{q,吨}(\mathfrak{秒}\mathfrak{升}(2|1))$作者：Ding 和 Feigin，当代。数学。248 , 83–108 (1998)，其中已发现基本W电流和屏蔽电流。在本文中，我们引入了更高的W电流并获得了它们之间的一组封闭的二次关系。这些关系独立于超代数的 Dynkin 图的选择$\mathfrak{秒}\mathfrak{升}(2|1)$，虽然屏蔽电流不是。这允许我们定义${\mathcal{宽}}_{q,吨}(\mathfrak{秒}\mathfrak{升}(2|1))$ 通过生成器和关系。