2007/06/30 by V. Boyko, Vyacheslav Boyko, Jiri Patera +2 · 1 citation
Mathematics · Physics and Astronomy · #Adjoint representation of a Lie algebra #Advanced Fiber Laser Technologies #Algebra over a field #Algebraic number #Cartan matrix #Diagonal #Geometry #Invariant (physics) #Invertible matrix #Kac–Moody algebra #Lie algebra #Lie conformal algebra #Mathematical analysis #Mathematical physics #Mathematics #Non-associative algebra #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Pure mathematics #Triangular matrix #math-ph #math.MP #math.RT #msc:17B05 #msc:17B10 #msc:17B30 #msc:22E70 #msc:58D19 #msc:81R05
paper · pdf · doi:10.1016/j.laa.2007.08.017
published as Linear Algebra Appl. 428 (2008), 834-854 · 21 pages, enhanced and extended version. Section 2 reviews the method of finding invariants of Lie algebras that was proposed in arXiv:math-ph/0602046 and arXiv:math-ph/0606045. The computation is based on developing a specific technique given in arXiv:0704.0937. Results generalize ones of arXiv:0705.2394 to the case of arbitrary relevant number of nilindependent elements
openalex publication_date 2007/11/27 · arxiv created 2018/04/01 · arxiv updated 2018/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The invariants of solvable Lie algebras with nilradicals isomorphic to the algebra of strongly upper triangular matrices and diagonal nilindependent elements are studied exhaustively. Bases of the invariant sets of all such algebras are constructed by an original purely algebraic algorithm based on Cartan's method of moving frames.