Contact Lie algebras of vector fields on the plane

Details Contact Lie algebras of vector fields on the plane Contact Lie algebras of vector fields on the plane

1999-03-15

arxiv.org/abs/math/9903198v1

Geom. Topol. 3 (1999), 1-20

Mathematics

Differential Geometry

20 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper1.abs.html

Scientific paper

The paper is devoted to the complete classification of all real Lie algebras of contact vector fields on the first jet space of one-dimensional submanifolds in the plane. This completes Sophus Lie's classification of all possible Lie algebras of contact symmetries for ordinary differential equations. As a main tool we use the abstract theory of filtered and graded Lie algebras. We also describe all differential and integral invariants of new Lie algebras found in the paper and discuss the infinite-dimensional case.

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