Studies on discrete integrable systems via tropical algebraic curves
| Project/Area Number |
26400107
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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 |
Basic analysis
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| Research Institution | Chiba University |
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Principal Investigator |
Nobe Atsushi 千葉大学, 教育学部, 准教授 (80397728)
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| Co-Investigator(Kenkyū-buntansha) |
間田 潤 日本大学, 生産工学部, 准教授 (80396853)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | トロピカル幾何学 / クラスター代数 / 戸田格子 / QRT系 / 楕円曲線 / 可積分系 / トロピカル代数曲線 / トロピカル楕円曲線 / 離散戸田格子 / アフィンLie代数 / 超離散化 |
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| Outline of Final Research Achievements |
First we considered Lie-algebraic generalizations of the Toda lattice. We realized the generalized Toda lattices of types A(2)2N, C(1)N and D(2)N as the sub-dynamical systems of the Toda lattices of types A(1)2N-1, A(1)2N, A(1)2N+1, respectively. We also obtained their tropical analogues.
Next we studied a tropical analogue of the Hessian group, which is the group of linear automorphisms acting on the Hesse pencil. We then obtained the dihedral group of degree 3 as the group of linear automorphisms acting on the tropical analogue of the Hesse pencil.
We moreover investigated the cluster algebras of rank 2 from the view point of discrete integrable systems. We gave the conserved quantities of the dynamical systems arising from the cluster algebras of types A1*A1, A2, B2, G2, A(1)1 and A(2)2. We also showed direct connections between the dynamical systems and the Mordell-Weil groups of the elliptic curves arising via the conserved quantities of the dynamical systems.
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Report
(5 results)
Research Products
(32 results)
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[Presentation] クラスター代数とQRT系2016
Author(s)
野邊厚，間田潤
Organizer
第12回 日本応用数理学会 研究部会連合発表会
Place of Presentation
神戸学院大学（兵庫県・神戸市）
Year and Date
2016-03-05
Related Report
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