Noncommutative differential calculus for Moyal subalgebras

TL;DR

This paper develops a differential calculus framework for Moyal subalgebras in R^4, enabling reduction and tensor product realization of forms, advancing noncommutative geometry methods.

Contribution

It introduces a method to construct differential calculus on Moyal subalgebras from a redundant calculus on the full algebra, facilitating geometric analysis.

Findings

Constructed a differential calculus for Moyal subalgebras.

Identified a frame of 1-forms enabling tensor product structure.

Provided a reduction approach suitable for noncommutative geometry applications.

Abstract

We build a differential calculus for subalgebras of the Moyal algebra on R^4 starting from a redundant differential calculus on the Moyal algebra, which is suitable for reduction. In some cases we find a frame of 1-forms which allows to realize the complex of forms as a tensor product of the noncommutative subalgebras with the external algebra Lambda^*.