Cauchy-Riemann Operators in Octonionic Analysis

TL;DR

This paper explores the properties of Cauchy-Riemann operators within octonionic analysis, focusing on algebraic structures, calculus, and symmetry groups related to octonion monogenic functions.

Contribution

It introduces the $e_4$-calculus and derives generalized Cauchy-Riemann systems for octonionic monogenic functions, expanding the theoretical framework.

Findings

Derived the $e_4$-calculus for octonions

Listed generalized Cauchy-Riemann systems in octonionic analysis

Identified symmetry groups associated with bilinear forms

Abstract

In this paper we first recall the definition of an octonion algebra and its algebraic properties. We derive the so called $e_4$-calculus and using it we obtain the list of generalized Cauchy-Riemann systems in octonionic monogenic functions. We define some bilinear forms and derive the corresponding symmetry groups.