Invariants and Automorphisms for slice regular functions

TL;DR

This paper explores the invariants of the automorphism group of slice regular functions over specific Clifford algebras, extending known algebra automorphism concepts to function spaces.

Contribution

It characterizes the invariants of automorphism groups for slice regular functions over Clifford algebras, a novel extension of algebra automorphism theory.

Findings

Describes automorphism group invariants for slice regular functions

Extends algebra automorphism concepts to function spaces

Provides new insights into Clifford algebra automorphisms

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 $Aut(A)$ 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 $A$.