Contraction based classification of supersymmetric extensions of kinematical Lie algebras

TL;DR

This paper explores how supersymmetric extensions of classical kinematical algebras can be systematically derived through contraction methods, revealing a hierarchical structure akin to classical classifications.

Contribution

It introduces a contraction-based framework for classifying supersymmetric extensions of kinematical algebras, extending classical contraction techniques to supersymmetry.

Findings

Contracting the supersymmetric anti-de Sitter algebra yields a hierarchy similar to Bacry-Lévy-Leblond classification.

The study demonstrates the structural relationship between different supersymmetric kinematical algebras.

The approach provides a systematic way to derive new supersymmetric algebras from known ones.

Abstract

We study supersymmetric extensions of classical kinematical algebras from the point of view of contraction theory. It is shown that contracting the supersymmetric extension of the anti-de Sitter algebra leads to a hierarchy similar in structure to the classical Bacry-L\'evy-Leblond classification