Construction of graded differential algebra with ternary differential

TL;DR

This paper constructs a graded q-differential algebra with a ternary differential satisfying d^3=0 and the q-Leibniz rule, based on first order differential calculus on complex algebras.

Contribution

It introduces a new graded q-differential algebra framework with ternary differential, expanding the algebraic structures in differential calculus.

Findings

Established the construction of graded q-differential algebra with ternary differential

Demonstrated the algebra satisfies d^3=0 and q-Leibniz rule

Built upon coordinate first order differential calculus on complex algebras

Abstract

In this article, we describe the construction of graded $q$-differential algebra with ternary differential satisfying the property $d^3=0$ and the $q$-Leibniz rule. Our starting point is coordinate first order differential calculus on some complex algebra and the corresponding bimodule of second order differentials.