2023 Fiscal Year Final Research Report
Morita equivalence for two algebras associated with dynamical Yang-Baxter maps
| Project/Area Number |
17K05187
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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 | Hokkaido University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2024-03-31
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| Keywords | ホップ亜代数 / ダイナミカル・ヤン・バクスター写像 |
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| Outline of Final Research Achievements |
By means of dynamical Yang-Baxter maps, we constructed Hopf algebroids whose base rings are arbitrary algebras. This result is published in Toyama Mathematical Journal (42, 2021, 51-72). In addition, we succeeded to present a systematic method to construct solutions to the reflection equation associated with the dynamical Yang-Baxter map satisfying suitable conditions. This result will be published in Toyama Mathematical Journal (Volume 44, 2023).
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| Free Research Field |
代数学
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| Academic Significance and Societal Importance of the Research Achievements |
本研究による成果の学術的意義は以下の通りである．（1）base ringが一般の場合に，ホップ亜代数を構成するための十分条件を明らかにした．（2）どんなテンソル圏に対しても適用可能であるような反射方程式の解の構成方法を提示した．（3）ダイナミカル・ヤン・バクスター写像から定まる反射方程式の解を組織的に構成した．（4）クイバー（quiver）のなすテンソル圏における反射方程式の解を構成した．
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