Geometry & Topology

Contact Lie algebras of vector fields on the plane

Boris M Doubrov and Boris P Komrakov

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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.

Article information

Geom. Topol., Volume 3, Number 1 (1999), 1-20.

Received: 19 May 1998
Revised: 27 November 1998
Accepted: 16 February 1999
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 17B66: Lie algebras of vector fields and related (super) algebras 53C30: Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]
Secondary: 34A26: Geometric methods in differential equations 58A20: Jets

contact vector fields filtered graded Lie algebras differential invariants


Doubrov, Boris M; Komrakov, Boris P. Contact Lie algebras of vector fields on the plane. Geom. Topol. 3 (1999), no. 1, 1--20. doi:10.2140/gt.1999.3.1.

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