kappa-deformed Spacetime From Twist

TL;DR

This paper constructs a new kappa-deformed spacetime by twisting the Hopf algebra of igl(n,R), resulting in a structure with larger symmetry than traditional kappa-Minkowski spacetime, and also derives a theta-deformed non-commutative spacetime.

Contribution

It introduces a novel twist of the igl(n,R) Hopf algebra to produce a kappa-deformed spacetime with enhanced symmetry properties.

Findings

Kappa-deformed spacetime with larger symmetry algebra.

Explicit coproducts of the twisted Hopf algebra.

Derivation of theta-deformed non-commutative spacetime.

Abstract

We twist the Hopf algebra of igl(n,R) to obtain the kappa-deformed spacetime coordinates. Coproducts of the twisted Hopf algebras are explicitly given. The kappa-deformed spacetime obtained this way satisfies the same commutation relation as that of the conventional kappa-Minkowski spacetime, but its Hopf algebra structure is different from the well known kappa-deformed Poincare algebra in that it has larger symmetry algebra than the kappa-Minkowski case. There are some physical models which consider this symmetry. Incidentally, we obtain the canonical (theta-deformed) non-commutative spacetime from canonically twisted igl(n,R) Hopf algebra.