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Contact Lie algebras of
vector fields on the plane
Boris M Doubrov and Boris P Komrakov |
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Geometry & Topology 3 (1999) 1–20
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DOI: 10.2140/gt.1999.3.1
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arXiv: math.DG/9903198 |
Abstract |
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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
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Mathematical Subject Classification
Primary: 17B66, 53C30
Secondary: 34A26, 58A20
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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
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Authors |
| Boris M Doubrov | |
| International Sophus Lie
Centre PO Box 70 220123 Minsk Belarus |
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| Boris P Komrakov | |
| International Sophus Lie
Centre PO Box 70 220123 Minsk Belarus |
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