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

2006/02/28 by Rutwig Campoamor-Stursberg · 3 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math-ph #math.MP

paper · pdf · doi:10.3842/sigma.2006.028

published as SIGMA 2 (2006), 028, 11 pages · Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

arxiv created 2006/02/28 · openalex publication_date 2006/02/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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).

Cited by

• Invariants of Lie algebras with fixed structure of nilradicals
• Invariants of triangular Lie algebras
• Invariants of solvable lie algebras with triangular nilradicals and diagonal nilindependent elements