Higher-dimensional kinematical Lie algebras via deformation theory

TL;DR

This paper classifies higher-dimensional kinematical Lie algebras and their deformations using deformation theory, identifying those with invariant inner products, thus advancing the understanding of their algebraic structures.

Contribution

It provides a systematic classification of kinematical Lie algebras in dimensions four and above, including their deformations and invariant inner products, which was previously incomplete.

Findings

Classified kinematical Lie algebras in D ≥ 4

Identified deformations of static and central extension Lie algebras

Determined which Lie algebras admit invariant inner products

Abstract

We classify kinematical Lie algebras in dimension $D \geq 4$. This is approached via the classification of deformations of the relevant static kinematical Lie algebra. We also classify the deformations of the universal central extension of the static kinematical Lie algebra in dimension $D\geq 4$. In addition we determine which of these Lie algebras admit an invariant inner product.