2006/02/28 by V. Boyko, Vyacheslav Boyko, Jiri Patera +3 · 47 citations
Mathematics · Physics and Astronomy · #Adjoint representation of a Lie algebra #Advanced Differential Geometry Research #Affine Lie algebra #Algebra over a field #Algorithm #Automorphism #Computation #Current algebra #Killing form #Lie algebra #Lie conformal algebra #Lie group #Mathematics #Non-associative algebra #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Pure mathematics #Real form #Representation of a Lie group #Representation theory #math-ph #math.MP #math.RT #msc:17B05 #msc:17B10 #msc:17B30 #msc:22E70 #msc:58D19 #msc:81R05
paper · pdf · doi:10.1088/0305-4470/39/20/009
published in Journal of Physics A Mathematical and General 39(20), 5749-5762 (Institute of Physics) · 17 pages, extended version
openalex publication_date 2006/05/03 · arxiv created 2010/02/23 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A new purely algebraic algorithm is presented for computation of invariants (generalized Casimir operators) of Lie algebras. It uses the Cartan method of moving frames and the knowledge of the group of inner automorphisms of each Lie algebra. The algorithm is applied, in particular, to computation of invariants of real low-dimensional Lie algebras. A number of examples are calculated to illustrate its effectiveness and to make a comparison with the same cases in the literature. Bases of invariants of the real six-dimensional solvable Lie algebras with four-dimensional nilradicals are newly calculated and listed in a table.