The quantum Poincare group from quantum group contraction

TL;DR

This paper introduces a contraction method for the de Sitter quantum group to derive the quantum Poincare group across dimensions, highlighting its bicrossproduct structure and duality with the -Poincare9 algebra.

Contribution

It presents a novel contraction approach from de Sitter to Poincare quantum groups, elucidating their algebraic structures and dualities.

Findings

Derived quantum Poincare group via contraction method.

Established bicrossproduct structure of the quantum Poincare group.

Showed duality with b7Poincare9 Hopf algebra in two dimensions.

Abstract

We propose a contraction of the de Sitter quantum group leading to the quantum Poincare group in any dimensions. The method relies on the coaction of the de Sitter quantum group on a non--commutative space, and the deformation parameter $q$ is sent to one. The bicrossproduct structure of the quantum Poincar\'e group is exhibited and shown to be dual to the one of the $\kappa$--Poincar\'e Hopf algebra, at least in two dimensions.