Invariants and automorphisms for slice regular functions

Abstract

Let $A$ be one of the following Clifford algebras: ${\mathbb{R}}_2\cong \mathbb{H}$ or ${\mathbb{R}}_3$. For the algebra $A$, the automorphism group $\mathrm{Aut}(A)$ and its invariants are well known. In this paper, we will describe the invariants of the automorphism group of the algebra of slice regular functions over $A$.