2002/08/26 by Rutwig Campoamor-Stursberg · 23 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Casimir effect #Combinatorics #Dimension (graph theory) #Fundamental representation #Lie algebra #Mathematics #Physics #Pure mathematics #Quantum mechanics #Sphingolipid Metabolism and Signaling #math-ph #math.MP #math.RA #msc:17B05 #msc:17B10
paper · pdf · doi:10.1088/0305-4470/36/5/312
published in Journal of Physics A Mathematical and General 36(5), 1357-1369 (Institute of Physics) · 16 pages
arxiv created 2002/08/26 · openalex publication_date 2003/01/22 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
We analyse the number 𝒩 of functionally independent generalized Casimir invariants for non-semisimple Lie algebras 𝔰→/⊕ R 𝔯 with Levi factors isomorphic to 𝔰𝔬(3) and 𝔰𝔩(2, ℝ) in dependence of the pair ( R , 𝔯) formed by a representation R of 𝔰 and a solvable Lie algebra 𝔯. We show that for any dimension n ⩾ 6, there exist Lie algebras 𝔰→/⊕ R 𝔯 with non-trivial Levi decomposition such that (𝒩(𝔰→/⊕ R 𝔯) = 0.