On Lie's classification of subalgebras of vector fields on the plane
Hassan Azad, Indranil Biswas, Fazal M. Mahomed, and Said Waqas Shah
TL;DR
This paper provides a concise proof of Lie's classification of solvable vector field algebras on the plane, utilizing fundamental representation theory and partial differential equations to clarify the structure.
Contribution
It offers a simplified proof of Lie's classification, emphasizing the use of basic representation theory and PDEs, which enhances understanding of solvable vector field algebras.
Findings
Classification of solvable vector field algebras on the plane
Simplified proof using representation theory and PDEs
Clarification of algebraic structures
Abstract
A brief proof of Lie's classification of solvable algebras of vector fields on the plane is given. The proof uses basic representation theory and PDEs.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models