The Unification of Nonassociative Structures

TL;DR

This paper explores methods to unify various non-associative and associative algebraic structures, aiming to create a comprehensive framework for understanding their relationships.

Contribution

It introduces new approaches to unify Lie, Jordan, and associative algebras within a single theoretical framework.

Findings

Proposes a unified algebraic structure encompassing Lie and Jordan algebras

Establishes connections between different non-associative algebra classes

Provides a foundation for further algebraic unification research

Abstract

The main non-associative algebras are Lie algebras and Jordan algebras. There are several ways to unify these non-associative algebras and associative algebras.