Transitive Lie algebras of vector fields: an overview

DOI10.1007/s12346-011-0062-9zbMath1365.17014arXiv1107.2836OpenAlexW2109970517MaRDI QIDQ1936477

Jan Draisma

Publication date: 5 February 2013

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.2836

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras (17-02)

Related Items

Projectable Lie algebras of vector fields in 3D, On nilpotent and solvable Lie algebras of derivations, Unnamed Item, Unnamed Item, Unnamed Item, Solvable Lie algebras of vector fields and a Lie's conjecture

Uses Software

• GAP
• LiE

Cites Work

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• The infinite groups of Lie and Cartan. I: The transitive groups
• Infinite dimensional primitive Lie algebras
• Lectures on quadratic Jordan algebras
• Lie symmetries and differential Galois groups of linear equations
• The maximal subgroups of the classical groups
• Semisimple subalgebras of semisimple Lie algebras
• Algorithms for reducing a system of PDEs to standard form, determining the dimension of its solution space and calculating its Taylor series solution
• Finding abstract Lie symmetry algebras of differential equations without integrating determining equations
• Induced and Produced Representations of Lie Algebras
• Lie Algebras of Vector Fields in the Real Plane
• Lie Algebras of Differential Operators in Two Complex Variables
• An algebraic model of transitive differential geometry
• Simple Lie algebras over fields of positive characteristic. I: Structure theory
• Recognizing the symmetry type of O. D. E. s
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