Universal differential calculus on ternary algebras

TL;DR

This paper introduces the concept of ternary algebras, defines their universal envelope and tri-modules, and develops a universal differential calculus with foundational properties, expanding algebraic frameworks.

Contribution

It presents the first comprehensive framework for differential calculus on ternary algebras, including universal envelopes and tri-modules, which were not previously established.

Findings

Defined universal envelope of ternary algebras

Introduced tri-modules over ternary algebras

Developed basic properties of universal differential calculus

Abstract

General concept of ternary algebras is introduced in this article, along with several examples of its realization. Universal envelope of such algebras is defined, as well as the concept of tri-modules over ternary algebras. The universal differential calculus on these structures is then defined and its basic properties investigated.