Differential structure on kappa-Minkowski space, and kappa-Poincare algebra

TL;DR

This paper develops realizations of the $ppa$-Minkowski space and $ppa$-Poincare9 algebra using formal power series, establishing a differential calculus compatible with Lorentz symmetry that differs from traditional bicovariant approaches.

Contribution

It introduces new realizations of the $ppa$-Poincare9 algebra and constructs a differential calculus on $ppa$-Minkowski space with the same dimension as the space itself.

Findings

Realizations of generators as formal power series in the Weyl algebra.

Hopf algebra structure related to different realizations.

A differential calculus with one-forms matching the space dimension.

Abstract

We construct realizations of the generators of the $\kappa$-Minkowski space and $\kappa$-Poincar\'{e} algebra as formal power series in the $h$-adic extension of the Weyl algebra. The Hopf algebra structure of the $\kappa$-Poincar\'{e} algebra related to different realizations is given. We construct realizations of the exterior derivative and one-forms, and define a differential calculus on $\kappa$-Minkowski space which is compatible with the action of the Lorentz algebra. In contrast to the conventional bicovariant calculus, the space of one-forms has the same dimension as the $\kappa$-Minkowski space.