2019 Fiscal Year Final Research Report
Gepmrtic study of quantum groups and its applications
| Project/Area Number |
16K05055
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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 | Rikkyo University (2017-2019)
The University of Tokyo (2016) |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Keywords | 量子包絡代数 |
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| Outline of Final Research Achievements |
In resent study of mathematical physics (string theory, especially), it is known that toroidal Lie algebras (LTA), and quantum toroidal algebras (QTA) play important roles. In this reseach project, we investigate the structure of these algebras in uniform way, by using the theory of elliptic root systems. Especially, we prove that these algebras have an elliptic modular group action induced from one on elliptic root systems. We believe these properties are quite
important in the future study of these algebras.
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| Free Research Field |
代数学
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| Academic Significance and Societal Importance of the Research Achievements |
本研究の対象となるTLA及びQTAは，近年弦理論を始めとして様々な分野で注目を浴びている代数系であるが，既存の手法が殆ど役に立たないとの理由から組織的な研究は殆ど行われて来なかった．本研究では楕円ルート系の理論を用いてこの代数系を調べ，楕円モジュラー群がTLA, QTAに作用することを示した．これは，既存のルート系の理論，リー代数，量子包絡代数には無かった全く新しい性質であり，今後の当該代数の研究に重要な役割を果たすことが期待される．
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