Quantum Algebras for Maximal Motion Groups of N-Dimensional Flat Spaces

TL;DR

This paper introduces a unified embedding method to generate q-deformations of non-semisimple algebras associated with motion groups in N-dimensional flat spaces, encompassing various classical algebras through contractions.

Contribution

It presents a global scheme for q-deformation applicable to all iso(p,q) algebras and their contractions, unifying the deformation process for multiple motion groups.

Findings

Provides a systematic method for q-deformation of motion algebra groups.

Applies to Euclidean, Poincaré, and Galilei algebras via contractions.

Enables consistent deformation across different N-dimensional flat space symmetries.

Abstract

An embedding method to get $q$-deformations for the non--semisimple algebras generating the motion groups of $N$--dimensional flat spaces is presented. This method gives a global and simultaneous scheme of $q$-deformation for all $iso(p,q)$ algebras and for those ones obtained from them by some In\"on\"u--Wigner contractions, such as the $N$--dimensional Euclidean, Poincar\'e and Galilei algebras.