2022 Fiscal Year Final Research Report
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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| 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 |
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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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| Free Research Field |
代数学
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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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