On Hermitian and skew-Hermitian matrix algebras over octonions

TL;DR

This paper investigates the algebraic structures of Hermitian and skew-Hermitian matrices over octonions, establishing their simplicity and analyzing derivations and associative forms.

Contribution

It provides the first detailed analysis of simplicity, derivations, and associative forms for these specific octonionic matrix algebras.

Findings

Proved the simplicity of Hermitian and skew-Hermitian octonionic matrix algebras.

Computed $ ext{delta}$-derivations for these algebras.

Identified symmetric associative forms within these algebraic structures.

Abstract

We prove simplicity, and compute $\delta$-derivations and symmetric associative forms of algebras in the title.