| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
|
|---|
| Outline of Final Research Achievements |
The set of Hamiltonian vector fields from a Poisson structure consists a Lie algebra. Gel'fand-Fukｓ theory dealt with (co)chain complex and (co)homology groups of those Lie algebras and reduced general discussions to finite dimensional ones by using "weight". In our research project, we got results in 3 branches.
(1) In the relative GF-cohomology group of formal Hamiltonian vector fields on the 2-plane of weight 24, we identified all the Betti numbers after a long calculation of more than five years. There are 3 independent cycles in degree 7. (2) We modified the weight and developed Gel'fand-Fuks type theory for not only symplectic but also Poisson structures of homogeneous polynomial coefficients on vector space. (3) By Schouten bracket, the set of multivector fields of various degrees forms a Z-graded Lie superalgebra. We introduced a notion of "double weight" and obtained examples of polynomial coefficient multivector fields on n-dimensional vector space.
|
