Geometry & Topology 3 (1999) 1–20

DOI: 10.2140/gt.1999.3.1

arXiv: math.DG/9903198

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

contact vector fields, filtered, graded Lie algebras, differential invariants

Mathematical Subject Classification

Primary: 17B66, 53C30

Secondary: 34A26, 58A20

References

Forward citations

Publication

Received: 19 May 1998
Revised: 27 November 1998
Accepted: 16 February 1999
Published: 15 March 1999
Proposed: Frances Kirwan
Seconded: Simon Donaldson, Robion Kirby

Authors