Fundamentals of rooted tree maps and study on multiple zeta values
| Project/Area Number |
19K03434
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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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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Kyoto Sangyo University |
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Principal Investigator |
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| Project Period (FY) |
2019-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2022: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2021: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 根付き木写像 / 多重ゼータ値 / 多重L値 / Hopf代数 / 調和積代数 / 補間多重L値 / 調和積 / 根付き木Hopf代数 / 一般導分作用素 / t-多重L値 / Connes-KreimerのHopf代数 |
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| Outline of Research at the Start |
根付き木のなすConnes-KreimerのHopf代数の二変数非可換多項式環へのある作用を発見し、根付き木写像と呼んでいる。根付き木写像が多重ゼータ値の間の広い関係式族を誘導することを証明済みであるが、本現象の根本原理を解明できていない。そこで、本研究では根付き木写像の代数的な基礎理論を整備する。さらに、根付き木写像の代数的拡張や数理物理的な応用も探究する。
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| Outline of Final Research Achievements |
Based on Connes-Kreimer Hopf algebra of rooted trees, rooted tree maps was defined around 2018. They are closely related with multiple zeta values. This research makes some of their fundamentals clear. In particular, we got results on interpretation of rooted tree maps by means of harmonic algebra, explicit representation of antipode maps, and generalization of rooted tree maps applicable to multiple L-values.
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| Academic Significance and Societal Importance of the Research Achievements |
根付き木写像は, 多重ゼータ値の代数的理論に新たな切り口を与えた. perturbative QFTやFeynman物理学と多重ゼータ値論との関連を示唆する現象の一つとしても, 根付き木写像は学術的に興味深い. その純代数的な性質や拡張の可能性に関する本成果は十分に意義がある.
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Report
(5 results)
Research Products
(7 results)
