Geodesic
Finite-Dimensional Subalgebras of the Lie Algebra of Vector Fields on the Circle
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 338-342 
M. S. Strigunova. Finite-Dimensional Subalgebras of the Lie Algebra of Vector Fields on the Circle. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 338-342. http://geodesic.mathdoc.fr/item/TM_2002_236_a34/
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     title = {Finite-Dimensional {Subalgebras} of the {Lie} {Algebra} of {Vector} {Fields} on the {Circle}},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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 $\mathrm {sl}_2(\mathbb R)$.

[1] Zhelobenko D. P., Kompaktnye gruppy Li i ikh predstavleniya, Nauka, M., 1970 | MR | Zbl

[2] Zhelobenko D. P., Shtern A. I., Predstavleniya grupp Li, Nauka, M., 1983 | MR

[3] Barut A., Ronchka R., Teoriya predstavlenii grupp i ee prilozheniya, Mir, M., 1980 | Zbl

[4] Pressli A., Sigal G., Gruppy petel, Mir, M., 1990 | MR