Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 2 (2006), 028, 11 pages      math-ph/0602065      https://doi.org/10.3842/SIGMA.2006.028

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

Rutwig Campoamor-Stursberg
Departamento Geometría y Topología, Fac. CC. Matemáticas U.C.M., Plaza de Ciencias 3, E-28040 Madrid, Spain

Received November 06, 2005, in final form February 14, 2006; Published online February 28, 2006

Abstract
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).

Key words: Casimir operator; characteristic polynomial; Lie algebra; missing label; kinematical group.

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