Application of cluster algebras to difference equations and 3-manifolds
| Project/Area Number |
26400037
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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 |
Algebra
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| Research Institution | Chiba University |
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Principal Investigator |
Yamazaki Rei 千葉大学, 大学院理学研究院, 准教授 (30431901)
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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 |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 数理物理学 / クラスター代数 / 可積分系 / 結び目不変量 / 幾何クリスタル / R行列 / ネットワーク / セルオートマトン / 量子クラスター代数 / 対称関数 / 差分方程式 / 双曲幾何 / 結び目 |
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| Outline of Final Research Achievements |
We have studied knot invariants and integrable difference equations by applying cluster algebras. We realized the braid group using cluster mutations on a punctured disk, and clarified the relation with Kashaev's R-matrix via quantum cluster algebra. We studied the symplectic structure for the difference equations associated with exchange matrices of period one. We introduced a generalization of the discrete Toda lattice equation by using the network model on a torus, and solved its initial value problem using algebraic geometry and combinatorics. Further, we constructed the symmetric group action on a quiver on a cylinder, and studied the geometric R-matrix of A-type from the view point of cluster algebra.
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Report
(5 results)
Research Products
(26 results)
