Quantization of Galois theory
| Project/Area Number |
25610004
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Nagoya University |
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Principal Investigator |
Umemura Hiroshi 名古屋大学, 多元数理科学研究科, 名誉教授 (40022678)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | Picard-Vessiot 理論 / 量子ガロア理論 / Hopf 代数 / ガロア理論 / 量子化 / Picard-Vessiot理論 / 量子群 / テンソル圏 / 量子Picard-Vessiot理論 / Hopf代数 |
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| Outline of Final Research Achievements |
We can interpret differential Galois theory as a theory of Module algebras under the Hopf algebra of the co-orrdinate ring of the 1 dimensional additive group. Hopf algebraists succeeded in generalizing the theory of linear equations from this view point, to a co-commutative Hopf algebra acting on a commutative module algebra. There arises a natural question whether we can extend this general theory to non-commutative case, or we can quantize it. Using the notion of Galois hull born in our study of Galois theory of non-linear differential equations, we successfully established a general Galois theory of non-commutative linear equations with constant coefficients.
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Report
(4 results)
Research Products
(3 results)
