Invariants and Automorphisms for slice regular functions

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 $Aut(A)$ 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 $A$.