Application of the Gel'fand Matrix Method to the Missing Label Problem in Classical Kinematical Lie Algebras

Details Application of the Gel'fand Matrix Method to the Missing Label Problem in Classical Kinematical Lie Algebras Application of the Gel'fand Matrix Method to the Missing Label Problem in Classical Kinematical Lie Algebras

2006-02-28

arxiv.org/abs/math-ph/0602065v1

SIGMA 2 (2006), 028, 11 pages

Physics

Mathematical Physics

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Scientific paper

10.3842/SIGMA.2006.028

We briefly review a matrix based method to compute the Casimir operators of Lie algebras, mainly certain type of contractions of simple Lie algebras. The versatility of the method is illustrated by constructing matrices whose characteristic polynomials provide the invariants of the kinematical algebras in (3+1)-dimensions. Moreover it is shown, also for kinematical algebras, how some reductions on these matrices are useful for determining the missing operators in the missing label problem (MLP).

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