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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     author = {S. Mohammadzadeh and D. B. Fuchs},
     title = {Cohomology of the {Lie} {Algebra} $\mathfrak{H}_2$: {Experimental} {Results} and {Conjectures}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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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/