A group theoretic description of the $\kappa$-Poincar\'e Hopf algebra

TL;DR

This paper presents a novel group-theoretic approach to deriving the full $$-Poincaré Hopf algebra structure from the Iwasawa decomposition of $$ group, enhancing understanding of its algebraic foundations.

Contribution

It introduces a new method to obtain the $$-Poincaré Hopf algebra using group-theoretic manipulations based on the Iwasawa decomposition.

Findings

Full Hopf algebra structure derived from group-theoretic methods.

Connection established between $$-Poincaré algebra and $$ group decompositions.

Provides a clearer algebraic understanding of $$-Poincaré symmetry.

Abstract

It is well known in the literature that the momentum space associated to the $\kappa$-Poincar\'e algebra is described by the Lie group $\mathsf{A}\mathsf{N}(3)$. In this letter we show that the full $\kappa$-Poincar\'e 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.