Geometry & Topology, Vol. 3 (1999) Paper no. 1, pages 1--20.

Contact Lie algebras of vector fields on the plane

Boris M Doubrov, Boris P Komrakov

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 and graded Lie algebras, differential invariants

AMS subject classification. Primary: 17B66, 53C30. Secondary: 34A26, 58A20.

DOI: 10.2140/gt.1999.3.1

E-print: arXiv:math.DG/9903198

Submitted to GT on 19 May 1998. (Revised 27 November 1998.) Paper accepted 16 February 1999. Paper published 15 March 1999.

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Boris M Doubrov, Boris P Komrakov
International Sophus Lie Centre
PO Box 70, 220123 Minsk, Belarus
Email: Doubrov@islc.minsk.by, Komrakov@islc.minsk.by

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