Noncommutative multiplicative norm identities for the quaternions and the octonions

TL;DR

This paper introduces Capelli type identities that serve as noncommutative analogues of the multiplicative norm identities for quaternions and octonions, expanding the algebraic understanding of these structures.

Contribution

It presents new Capelli type identities for quaternions and octonions, providing a novel noncommutative framework for their multiplicative norm identities.

Findings

Established Capelli type identities for quaternions

Extended identities to octonions

Enhanced algebraic understanding of noncommutative norm relations

Abstract

We present Capelli type identities associated with the quaternions and the octonions, which are noncommutative versions of multiplicative norm identities for the quaternions and the octonions.