Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower weight Gel'fand-Kalinin-Fuks cohomology groups of the formal
  Hamiltonian vector fields on R^4   In this paper, we investigate the relative Gel'fand-Kalinin-Fuks cohomology
groups of the formal Hamiltonian vector fields on R^4. In the case of formal
Hamiltonian vector fields on R^2, we computed the relative
Gel'fand-Kalinin-Fuks cohomology groups of weight <20 in the paper by
Mikami-Nakae-Kodama. The main strategy there was decomposing the Gel'fand-Fucks
cochain complex into irreducible factors and picking up the trivial
representations and their concrete bases, and ours is essentially the same.
  By computer calculation, we determine the relative Gel'fand-Kalinin-Fuks
cohomology groups of the formal Hamiltonian vector fields on R^4 of weights 2,
4 and 6. In the case of weight 2, the Betti number of the cohomology group is
equal to 1 at degree 2 and is 0 at any other degree. In weight 4, the Betti
number is 2 at degree 4 and is 0 at any other degree, and in weight 6, the
Betti number is 0 at any degree.

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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg