On the conjugacy of pure imaginary elements of quaternion algebras and Cayley algebras

TL;DR

This paper investigates the conjugacy properties of pure imaginary elements with equal norm in quaternion and Cayley algebras, providing new insights into their algebraic structure.

Contribution

It presents new results on the conjugacy of pure imaginary elements in quaternion and Cayley algebras, extending understanding of their algebraic behavior.

Findings

Conjugacy results for pure imaginary elements with same norm in quaternion algebras.

Conjugacy results for pure imaginary elements with same norm in Cayley algebras.

Enhanced understanding of algebraic structure of quaternion and Cayley algebras.

Abstract

In the quatenions ($\H$, $\H'$, $\H^{C}$) and octonions ($\gC$, $\gC^\prime$, $\gC^C$), we show some results on the conjugacy of two pure imaginary non-zero elements with same norm.