Kinematical superalgebras and Lie algebras of order 3

TL;DR

This paper classifies kinematical algebras derived from Lie superalgebras and Lie algebras of order three, exploring their relationships through generalized contractions from known algebraic structures.

Contribution

It provides a systematic classification of kinematical superalgebras and Lie algebras of order three, connecting them via generalized Inönü-Wigner contractions.

Findings

Classification of kinematical algebras from superalgebras and order three Lie algebras

Identification of relationships through generalized contractions

Connection to orthosymplectic superalgebra and de Sitter algebra

Abstract

We study and classify kinematical algebras which appear in the framework of Lie superalgebras or Lie algebras of order three. All these algebras are related through generalised Inon\"u-Wigner contractions from either the orthosymplectic superalgebra or the de Sitter Lie algebra of order three.