In this paper, we first define a supersymmetric Gelfand–Dickey hierarchy using the Sato equation. Then we introduce some time variables and derivations involving those that from a non-abelian Lie superalgebra. Next, we construct additional symmetries for the supersymmetric Gelfand–Dickey hierarchy with the aid of the Orlov–Schulman operators which involve the above time variables and dressing operators. We give the additional flow equations of the supersymmetric Gelfand–Dickey hierarchy, and prove that the additional flows are symmetries of the supersymmetric Gelfand–Dickey hierarchy. In this way, an isomorphism between the additional symmetries of the supersymmetric Gelfand–Dickey hierarchy and the super [Formula: see text] algebra is constructed. Finally, the [Formula: see text] type supersymmetric Gelfand–Dickey hierarchy is constructed and we consider the additional symmetries for the supersymmetric Gelfand–Dickey hierarchy with the [Formula: see text] type condition which is compatible with the flows of the [Formula: see text] type supersymmetric Gelfand–Dickey hierarchy.

中文翻译：

---

超对称 Gelfand-Dickey 层次结构的附加对称性

在本文中，我们首先使用 Sato 方程定义了一个超对称的 Gelfand-Dickey 层次结构。然后我们介绍了一些时间变量和涉及那些来自非阿贝尔李超代数的推导。接下来，我们借助涉及上述时间变量和修整算子的 Orlov-Schulman 算子为超对称 Gelfand-Dickey 层次结构构建额外的对称性。我们给出了超对称 Gelfand-Dickey 层次的附加流方程，并证明了附加流是超对称 Gelfand-Dickey 层次的对称性。这样，超对称 Gelfand-Dickey 层次结构的附加对称性和超 [公式：见正文] 代数之间的同构就被构建了。最后，[公式：