| Project/Area Number |
15K04856
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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 | Tokyo University of Science |
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Principal Investigator |
Yoshioka Akira 東京理科大学, 理学部第二部数学科, 教授 (40200935)
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| Co-Investigator(Renkei-kenkyūsha) |
MAEDA Yoshiaki 東北大学, 知の創出センター, 教授 (40101076)
MIYAZAKI Naoya 慶応義塾大学, 経済学部, 教授 (50315826)
KANAZAWA Tomoyo 東京理科大学, 理学部第二部数学科, 助教 (80713031)
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| Research Collaborator |
TAKEUCHI Tsukasa
HOSOKAWA Kiyonori
VISLASI Gaetano
LAMBIASE Gaetano
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | Deformation quantization / star product / star exponentials / convergent star product / noncommutative geometry / quantization / 変形量子化 / 非可換指数関数 / star exponential / シンプレクテイック幾何学 / ポアソン幾何学 / 量子化 / 非可換幾何学 / シンプレクティック幾何学 / 複素幾何学 |
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| Outline of Final Research Achievements |
We consider the algebra obtained by convergent star products. We study star exponentials defined in the algebra which are noncommutative or commutative. We have shown star exponentials of quadratic polynomials have singularities and we obtain several identities in the star product algebras using the singularities.
We also consider applications of star product algebras to geometry and mathematical physics. In star product algebras, transformation of expression is naturally introduced and then one has a flat connection. It is shown that the parallel transport in geometric quantization theory is equivalent to that of star product algebras with respect to the flat connection. We also obtain a geometric point of view of eigenvalue problem for operators via star product algebras and the Maslov quantization condition, and we consider a concrete model to which we can apply noncommutative geometry by star products.
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