Some remarks and properties of algebras obtained by the Cayley-Dickson process

TL;DR

This paper explores identities in algebras derived from the Cayley-Dickson process and investigates the spectral properties of matrices over these algebras, enhancing understanding of their algebraic structure.

Contribution

It introduces new identities in Cayley-Dickson algebras and analyzes the spectra of matrices with coefficients in these algebras, advancing algebraic theory.

Findings

Identities in alternative and Cayley-Dickson algebras identified

Spectral properties of matrices over these algebras analyzed

Contributions to understanding algebraic structures and matrix spectra

Abstract

Finding identities in nonassociative algebras plays an important role in the study of properties of these algebras. In this paper, we present some identities in alternative algebras and in algebras obtained by the Cayley-Dickson process. Moreover, the spectrum of matrices with coefficients in such algebras are investigated.