Generalized Poincare algebras, Hopf algebras and kappa-Minkowski spacetime

TL;DR

This paper develops a generalized framework for kappa-Poincare-Hopf algebras as symmetries of kappa-Minkowski spacetime, exploring deformations of Lorentz algebras and their physical implications.

Contribution

It introduces a unified description of kappa-Poincare-Hopf algebras, including a three-parameter family of deformed Lorentz generators and compatible deformations of related Hopf algebras.

Findings

Unique kappa-Poincare-Hopf algebra with undeformed Lorentz algebra identified

Constructed a three-parameter family of deformed Lorentz generators

Presented deformation of igl(4) Hopf algebra compatible with kappa-Minkowski

Abstract

We propose a generalized description for the kappa-Poincare-Hopf algebra as a symmetry quantum group of underlying kappa-Minkowski spacetime. We investigate all the possible implementations of (deformed) Lorentz algebras which are compatible with the given choice of kappa-Minkowski algebra realization. For the given realization of kappa-Minkowski spacetime there is a unique kappa-Poincare-Hopf algebra with undeformed Lorentz algebra. We have constructed a three-parameter family of deformed Lorentz generators with kappa-Poincare algebras which are related to kappa-Poincare-Hopf algebra with undeformed Lorentz algebra. Known bases of kappa-Poincare-Hopf algebra are obtained as special cases. Also deformation of igl(4) Hopf algebra compatible with the kappa-Minkowski spacetime is presented. Some physical applications are briefly discussed.