This article is cited in 1 paper

Finite-Dimensional Subalgebras of the Lie Algebra of Vector Fields on the Circle

M. S. Strigunova

M. V. Lomonosov Moscow State University

Abstract: Finite-dimensional subalgebras of the Lie algebra $\mathrm {Vect}(S^1)$ of smooth tangent vector fields on the circle are considered that consist of analytic vector fields. It is proved that (up to an isomorphism) there are only three such subalgebras: a one-dimensional subalgebra, a two-dimensional noncommutative subalgebra, and a three-dimensional subalgebra isomorphic to $\mathrm {sl}_2(\mathbb R)$.

UDC: 517.9

Received in January 2001

 English version: Proceedings of the Steklov Institute of Mathematics, 2002, 236, 325–329

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