On certain three algebras generated by binary algebras

TL;DR

This paper investigates the existence of n-algebras with multiplication not reducible to binary operations and explores their isomorphism properties, using a novel classification approach.

Contribution

It introduces a new method for classifying algebras and demonstrates the existence of complex n-algebras with unique multiplication properties.

Findings

Existence of n-algebras with non-binary multiplication

Non-isomorphic algebras can have similar 3-algebra properties

New classification approach effective for algebra problems

Abstract

This paper's central theme is to prove the existence of an n-algebra whose multiplication cannot be expressed employing any binary operation. Furthermore, to prove if two algebras are not isomorphic, this property does not hold for $3$-algebras corresponding to these two algebras. The proof drives applying some results gotten early applying a new approach for the classification algebras problem, introduced recently, which showed great success in solving many classification algebras problems.