On the classification of metric hypercomplex group alternative-elastic algebras for n=8

TL;DR

This paper addresses the classification and construction of metric hypercomplex group alternative-elastic algebras for n=8, clarifying their relation to symmetric controlling spinors and octonions.

Contribution

It provides a detailed classification method for these algebras and explains how to associate and construct symmetric controlling spinors for n=8.

Findings

Classification scheme for n=8 hypercomplex algebras

Method to construct symmetric controlling spinors

Description of octonion class within these algebras

Abstract

In this article, the clarification to Note 4 (arXiv:1202.0941) for n=8 is considered. In this connection, answers to the following questions are given. 1. How to classify the metric hypercomplex orthogonal group alternative-elastic algebras for n=8? 2. How to associate the metric hypercomplex orthogonal group alternative-elastic algebra to the symmetric controlling spinor for n=8? 3. How technically to construct the symmetric controlling spinor for n=8? 4. What class does the octonion belong to, and how to describe its?