Lie algebras with finite-dimensional polynomial centralizer

DOI10.1016/S0022-247X(02)00037-9zbMath1032.17043OpenAlexW2064186035MaRDI QIDQ1614679

Giuseppe Gaeta, Sebastian Walcher

Publication date: 8 September 2002

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-247x(02)00037-9

zbMATH Keywords

centralizerpolynomial invariantsPoincaré-Dulac normal formelementary solutionsLie algebra of polynomial vector fieldsapplications to normal forms

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Lie algebras of vector fields and related (super) algebras (17B66) Symmetries, invariants of ordinary differential equations (34C14) Structure theory for Lie algebras and superalgebras (17B05)

Cites Work

• Nonlinear equations with superposition principles and the theory of transitive primitive Lie algebras
• Nonlinear action of Lie groups and superposition principles for nonlinear differential equations
• On differential equations in normal form
• Convergence of normal form transformations: The Role of symmetries
• Geometric invariant theory in a model-independent analysis of spontaneous symmetry and supersymmetry breaking
• On the convergence of normalizing transformations in the presence of symmetries
• Decomposition of differential equations
• Classification of systems of nonlinear ordinary differential equations with superposition principles
• Comments on superposition rules for nonlinear coupled first-order differential equations
• Über polynomiale, insbesondere Riccatische, Differentialgleichungen mit Fundamentallösungen. (On polynomials, especially Riccati polynomials, differential equations with fundamental solutions)
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