Volume 3, issue 1 (1999)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Contact Lie algebras of vector fields on the plane

Boris M Doubrov and Boris P Komrakov

Geometry & Topology 3 (1999) 1–20

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
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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
Boris M Doubrov
International Sophus Lie Centre
PO Box 70
220123 Minsk
Belarus
Boris P Komrakov
International Sophus Lie Centre
PO Box 70
220123 Minsk
Belarus