2022-01-18T11:48:58Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000400172021-03-02T02:39:35ZLower Weight Gel’fand-Kalinin-Fuks Cohomology Groups of the Formal Hamiltonian Vector Fields on R4Mikami, Kentaro92454Nakae, Yasuharu92455415In this paper, we investigate the relative Gel’fand- Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields on R4. In the case of formal Hamiltonian vector fields on R2, 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 R4 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.departmental bulletin paperGraduate School of Mathematical Sciences, The University of Tokyo2013-03-15application/pdfJournal of mathematical sciences, the University of Tokyo419699716AA1102165313405705https://repository.dl.itc.u-tokyo.ac.jp/record/40017/files/jms190409.pdfeng