Studies of algebro-geometric aspects on dynamical Yang-Baxter maps

• Project/Area Number: 19540001
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Hokkaido University
• Principal Investigator: SHIBUKAWA Youichi Hokkaido University, 大学院・理学研究院, 准教授 (90241299)
• Project Period (FY): 2007 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2007: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• 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 / ダイナミカルヤンバラスター写像 / 量子代数 / L作用素 / ダイナミカル表現

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.

Research Products

• [Journal Article] Mitsuhiro Takeuchi, FRT construction for dynamical Yang-Baxter maps (2010)
  • Author(s): Youichi Shibukawa
  • Journal Title: Journal of Algebra 323 Pages: 1698-1728
  • Peer Reviewed
• [Journal Article] FRT construction for dynamical Yang-Baxter maps (2010)
  • Author(s): Youichi Shibukawa
  • Journal Title: Journal of Algebra 323 Pages: 1698-1728
  • Peer Reviewed
• [Journal Article] ダイナミカル・ヤン・バクスター写像 (2009)
  • Author(s): 澁川陽一
  • Journal Title: 京都大学数理解析研究所講究録 1647 Pages: 81-96
• [Journal Article] ダイナミカル・ヤン・バクスター写像 (2009)
  • Author(s): 澁川陽一
  • Journal Title: 数理解析研究所講究録 1647 Pages: 81-96
• [Presentation] (H, X)-bialgebroids associated with dynamical Yang-Baxter maps (2008)
  • Author(s): 澁川陽一
  • Organizer: 組合せ論的表現論の拡がり
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-10-09
• [Presentation] (H, X)-bialgebroids associated with dynamical Yang-Baxter maps (2008)
  • Author(s): 澁川陽一
  • Organizer: 日本数学会(無限可積分系セッション)
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-25
• [Presentation] Bialgebroids related to dynamical Yang-Baxter maps (2008)
  • Author(s): Youichi Shibukawa
  • Organizer: Noncommutative Structures-in Mathematics and Physics
  • Place of Presentation: ベルギー・ブリュッセル, Paleis der Academien
  • Year and Date: 2008-07-22
• [Presentation] (H, X)-bialgebroids associated with dynamical Yang-Baxter maps and their dynamical representations (2008)
  • Author(s): Youichi Shibukawa
  • Organizer: 組合せ論的表現論の拡がり
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] (H, X)-bialgebroids associated with dynamical Yang-Baxter maps (2008)
  • Author(s): Youichi Shibukawa
  • Organizer: 日本数学会無限可積分系セッション
  • Place of Presentation: 東京工業大学
• [Presentation] Bialgebroids related to dynamical Yang-Baxter maps (2008)
  • Author(s): Youichi Shibukawa
  • Organizer: Noncommutative Structures in Mathematics and Physics
  • Place of Presentation: ベルギー・ブリュッセル・Paleis der Academien
• [Presentation] Dynamical Yang-Baxter maps with an invariance condition (2008)
  • Author(s): Youichi Shibukawa
  • Organizer: SNU-HU 5th joint Symposium on Mathematics
  • Place of Presentation: 韓国・ソウル・ソウル大学校
• [Presentation] Dynamical Yang-Baxter maps (2007)
  • Author(s): Youichi Shibukawa
  • Organizer: Enigma conference on Mathematical Physics
  • Place of Presentation: Royal Institute of Technol-ogy, Stockholm, Sweden
  • Year and Date: 2007-06-28
• [Presentation] Dynamical Yang-Baxter maps (2007)
  • Author(s): Youichi Shibukawa
  • Organizer: Enigma Conference on Mathematical Physics
  • Place of Presentation: スウェーデン・ストックホルム・Royal Institute of Technology