Contact Lie algebras of vector fields on the plane
Differential Geometry
2014-11-11 v1 Representation Theory
Abstract
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.
Keywords
Cite
@article{arxiv.math/9903198,
title = {Contact Lie algebras of vector fields on the plane},
author = {Boris M. Doubrov and Boris P. Komrakov},
journal= {arXiv preprint arXiv:math/9903198},
year = {2014}
}
Comments
20 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper1.abs.html