A new differential calculus on noncommutative spaces

TL;DR

This paper introduces a new differential calculus framework on a two-dimensional noncommutative quantum space, maintaining invariance under the quantum group $GL_{qp}(2)$, with differentials behaving as bosonic entities.

Contribution

It develops a $GL_{qp}(2)$ invariant differential calculus on a noncommutative quantum space with bosonic differentials, expanding the mathematical tools for quantum geometry.

Findings

Invariant differential calculus constructed for the quantum space

Differentials exhibit bosonic commutative properties

Framework enhances understanding of noncommutative geometries

Abstract

We develop a $GL_{qp}(2)$ invariant differential calculus on a two-dimensional noncommutative quantum space. Here the co-ordinate space for the exterior quantum plane is spanned by the differentials that are commutative (bosonic) in nature.