Invariants of triangular Lie algebras

2007/04/30 by V. Boyko, Vyacheslav Boyko, Jiri Patera +3 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebra over a field #Lie algebra #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #math-ph #math.MP #math.RT #msc:17B05 #msc:17B10 #msc:17B30 #msc:22E70 #msc:58D19 #msc:81R05

paper · pdf · doi:10.1088/1751-8113/40/27/009

published as J. Phys. A 40 (2007) 7557-7572 · LaTeX2e, 16 pages; misprints are corrected, some proofs are extended

openalex publication_date 2007/06/19 · arxiv created 2007/09/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants (‘generalized Casimir operators’) are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras.

Citations

• Moving Coframes: II. Regularization and Theoretical Foundations
• Moving Coframes: I. A Practical Algorithm
• A class of solvable Lie algebras and their Casimir invariants
• Application of the Gel'fand Matrix Method to the Missing Label Problem in Classical Kinematical Lie Algebras
• Computation of invariants of Lie algebras by means of moving frames
• Invariants of Lie algebras with fixed structure of nilradicals

Cited by

• Invariants of solvable lie algebras with triangular nilradicals and diagonal nilindependent elements
• Invariants of Lie algebras via moving frames

Related

• Invariants of triangular Lie algebras with one nilindependent diagonal element
• Invariants of solvable lie algebras with triangular nilradicals and diagonal nilindependent elements
• Invariant theory and coefficient algebras of Lie algebras
• Generalized Casimir invariants of six dimensional solvable real Lie algebras with five dimensional nilradical
• Gradings on the algebra of triangular matrices as a Lie algebra: revisited