A group theoretic description of the $\kappa$-Poincaré Hopf algebra

Abstract

It is well known in the literature that the momentum space associated to the $\kappa$-Poincaré algebra is described by the Lie group $\mathsf{AN}(3)$. In this letter we show that the full $\kappa$-Poincaré Hopf algebra structure can be obtained from rather straightforward group-theoretic manipulations starting from the Iwasawa decomposition of the of the $\mathsf{SO}(1,4)$ group.

16 pages, no figures. Minor editing, references added

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• Asymmetry in momentum space: restoring $\mathcal{C}\mathcal{P}\mathcal{T}$ invariance of $\kappa$-field theory