Geodesic
Cohomology of the Lie Algebra $\mathfrak{H}_2$: Experimental Results and Conjectures
Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 2, pp. 67-78.

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The cohomology with trivial coefficients of the Lie algebra $\mathfrak{H}$ of Hamiltonian vector fields in the plane and of its maximal nilpotent subalgebra $L_1\mathfrak{H}$ is considered. The cohomology $H^2(L_1\mathfrak{H})$ is calculated, and some far-reaching conjectures concerning the cohomology of the Lie algebras mentioned above and based on an extensive experimental material are formulated.
Keywords: cohomology, Lie algebra, Hamiltonian vector field. 
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S. Mohammadzadeh; D. B. Fuchs. Cohomology of the Lie Algebra $\mathfrak{H}_2$: Experimental Results and Conjectures. Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 2, pp. 67-78. http://geodesic.mathdoc.fr/item/FAA_2014_48_2_a3/

[1] D. B. Fuks, Kogomologii beskonechnomernykh algebr Li, Nauka, M., 1984 | MR | Zbl

[2] I. M. Gelfand, D. I. Kalinin, D. B. Fuks, “O kogomologiyakh algebry Li gamiltonovykh formalnykh vektornykh polei”, Funkts. analiz i ego pril., 6:3 (1972), 25–29 | MR | Zbl

[3] J. Perchik, “Cohomology of Hamiltonian and related formal vector fields Lie algebras”, Topology, 15:4 (1976), 395–404 | DOI | MR | Zbl