Multiplicatively Ordered and Directed Hybrid Jordan-Lie Superalgebra

TL;DR

This paper introduces a novel algebraic structure that combines and extends properties of Jordan-Lie superalgebras and classical division rings, with potential implications for physics.

Contribution

It presents a new multiplicatively ordered and directed hybrid Jordan-Lie superalgebra, expanding the landscape of algebraic structures beyond traditional Lie and superalgebras.

Findings

The algebra generalizes key properties of Euclidean division rings.

It compares and contrasts with existing Jordan-Lie superalgebras.

Potential physical applications are suggested.

Abstract

A new algebra, hitherto not encountered in the usual Lie algebraic varieties or supervarieties, is introduced. The paper explores the rich and novel structure of the algebra, and it compares it on the one hand with the Jordan-Lie Superalgebras studied by Okubo and Kamiya, and on the other, with the four usual Euclidean division rings of the reals (R), the complexes (C), the quaternions (H) and the octonions (O), key algebraic properties of which the algebra is seen to combine, alter, extend and generalise. A potential physical application of the algebra is briefly alluded to at the end.