2013 Fiscal Year Final Research Report
Studies of cohomology groups in Poisson geometry
| Project/Area Number |
23540067
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Akita University |
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Principal Investigator |
MIKAMI KENTARO 秋田大学, 工学(系)研究科(研究院), 名誉教授 (70006592)
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| Project Period (FY) |
2011 – 2013
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| Keywords | ポアソン構造 / シンプレクティック構造 / 形式的ハミルトン・ベクトル場 / 運動量写像 / ゲルファント・フックス・コホモロジー群 / 既約分解 / 結晶基底(Crystal Basis) / グレブナー基底(Groebner Basis) |
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| Research Abstract |
I studied about Sp(2n) relative Gel'fand-Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields on the 2n-dimensional symplectic vector space ant got the results below. 1) In 2-dim case, we determined the GKF cohomology groups for weight 20. 2) In the case of 4-dim, using Littlewood-Richardson rule, we determined the GKF cohomology groups for weight 2,4 and 6. This was published in J.Math.Sci.Univ.Tokyo 19(2012)1-18, by the title Lower weight Gel'fand-Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields on R4. 3) By using crystal base theory, in 6-dimensional case, we studied the GKF cohomology groups for weight 2,4 and 6. The result is uploaded on http://arxiv.org by The relative Gel'fand-Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields on 6-dimensional plane, arXiv:1402.6834. 4) I gave an affirmative answer to a conjecture, and submitted to some Journal by the title, ``An affirmative answer to a conjecture for Metoki class''.
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Research Products
(7 results)
