2009 Fiscal Year Final Research Report
Studies of algebro-geometric aspects on dynamical Yang-Baxter maps
| Project/Area Number |
19540001
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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 |
SHIBUKAWA Youichi Hokkaido University, 大学院・理学研究院, 准教授 (90241299)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 双亜代数 / ダイナミカル・ヤン・バクスター写像 / テンソル圏 |
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| Research Abstract |
We constructed bialgebroids associated with dynamical Yang-Baxter maps, set-theoretic solutions to the quantum dynamical Yang-Baxter equation. Each bialgebroid provides with the tensor category consisting of its dynamical representations. This bialgebroid is a coalgebra object of a pre-tensor category ; and such category-theoretic properties give birth to the tensor category of dynamical representations. We also constructed the dynamical Yang-Baxter map by means of the principal homogeneous space.
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