In this paper we consider the symmetry behavior of slice monogenic functions under Möbius transformations. We describe the group under which slice monogenic functions are taken into slice monogenic functions. We prove a transformation formula for composing slice monogenic functions with Möbius transformations and describe their conformal invariance. Finally, we explain two construction methods to obtain automorphic forms in the framework of this function class. We round off by presenting a precise algebraic characterization of the subset of slice monogenic linear fractional transformations within the set of general Möbius transformations.

中文翻译：

---

切片单基因功能的对称性

在本文中，我们考虑了Möbius变换下的切片单基因函数的对称行为。我们描述了将切片单基因功能纳入切片单基因功能的类别。我们证明了用莫比乌斯变换组成单片函数的变换公式，并描述了它们的共形不变性。最后，我们在此函数类的框架中解释了两种构造方法以获得自构形式。我们通过呈现一般Möbius变换集中的切片单基因线性分数变换的子集的精确代数表征来结束。