Derivation based differential calculi for noncommutative algebras deforming a class of three dimensional spaces

TL;DR

This paper develops a derivation-based differential calculus for a family of Lie-type noncommutative algebras, reducing from a higher-dimensional Moyal space to better understand their geometric structure.

Contribution

It introduces a new derivation-based calculus for noncommutative algebras deforming three-dimensional spaces, connecting it to a higher-dimensional Moyal space.

Findings

Constructed a differential calculus using inner and outer derivations.

Reduced the calculus from four-dimensional Moyal space to three-dimensional algebras.

Provides a framework for analyzing geometric properties of noncommutative spaces.

Abstract

We equip a family of algebras whose noncommutativity is of Lie type with a derivation based differential calculus obtained, upon suitably using both inner and outer derivations, as a reduction of a redundant calculus over the Moyal four dimensional space.