Geometry & Topology

Contact Lie algebras of vector fields on the plane

Boris M Doubrov and Boris P Komrakov

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513883137

Digital Object Identifier
doi:10.2140/gt.1999.3.1

Mathematical Reviews number (MathSciNet)
MR1673271

Zentralblatt MATH identifier
0955.17016

Subjects
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

Keywords
contact vector fields filtered graded Lie algebras differential invariants

Citation

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. https://projecteuclid.org/euclid.gt/1513883137


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References

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