Kinematical Lie algebras in 2+1 dimensions
Tomasz Andrzejewski, Jos\'e Figueroa-O'Farrill
TL;DR
This paper classifies all kinematical Lie algebras in 2+1 dimensions by analyzing their deformations and identifying those with invariant symmetric inner products, providing a comprehensive structural understanding.
Contribution
It offers the first complete classification of 2+1 dimensional kinematical Lie algebras and identifies which admit invariant symmetric inner products.
Findings
Classified all kinematical Lie algebras in 2+1 dimensions.
Determined which algebras admit invariant symmetric inner products.
Provided deformation analysis of the static kinematical Lie algebra.
Abstract
We classify kinematical Lie algebras in dimension 2+1. This is approached via the classification of deformations of the static kinematical Lie algebra. In addition, we determine which kinematical Lie algebras admit invariant symmetric inner products.
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