Twisted conformal algebra related to $\kappa$-Minkowski space

TL;DR

This paper constructs twisted conformal algebra deformations related to $$-Minkowski space, demonstrating covariance of the noncommutative spacetime under these quantum symmetries and providing differential realizations.

Contribution

It introduces two new twisted conformal algebra deformations, extending the conformal algebra with noncommutative coordinates and their differential realizations.

Findings

Both deformations preserve covariance of $$-Minkowski space.

Explicit differential realizations of $$-Minkowski coordinates are provided.

The extended conformal algebra includes noncommutative coordinates.

Abstract

Twisted deformations of the conformal symmetry in the Hopf algebraic framework are constructed. The first one is obtained by a Jordanian twist built up from dilatation and momenta generators. The second is the light-like $\kappa$-deformation of the Poincare algebra extended to the conformal algebra, obtained by a twist corresponding to the extended Jordanian r-matrix. The $\kappa$-Minkowski spacetime is covariant quantum space under both of these deformations. The extension of the conformal algebra by the noncommutative coordinates is presented in two cases. The differential realizations for $\kappa$-Minkowski coordinates, as well as their left-right dual counterparts, are also included.