Solvable Lie Algebras of Vector Fields and a Lie's Conjecture

2019/07/31 by Katarzyna Grabowska, Janusz Grabowski
Mathematics · Physics and Astronomy · #Adjoint representation #Adjoint representation of a Lie algebra #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Conjecture #Graded Lie algebra #Killing form #Lie algebra #Lie conformal algebra #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Representation of a Lie group #Simple Lie group #math-ph #math.DG #math.GR #math.MP #msc:17B30 #msc:17B66 #msc:57R25 #msc:57S20

paper · pdf · doi:10.3842/sigma.2020.065

published as SIGMA 16 (2020), 065, 14 pages

arxiv created 2020/07/10 · openalex publication_date 2020/07/10 · arxiv updated 2020/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We present a local and constructive differential geometric description of finitedimensional solvable and transitive Lie algebras of vector fields. We show that it implies a Lie's conjecture for such Lie algebras. Also infinite-dimensional analytical solvable and transitive Lie algebras of vector fields whose derivative ideal is nilpotent can be adapted to this scheme.

Citations

• Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras
• Higher vector bundles and multi-graded symplectic manifolds