Research on variants of the polynomial invariant of Hopf algebras

• Project/Area Number: 22540058
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Kansai University
• Principal Investigator: WAKUI Michihisa 関西大学, システム理工学部, 准教授 (60252574)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000); Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: 代数学 / トポロジー / 環論 / 表現論 / ホップ代数 / 結び目

Research Abstract

Various variants of our polynomial invariant of Hopf algebras are introduced, and examined those properties. Computational results are obtained for several Hopf algebras. It is also showed that the Schodinger representation of the Drinfel'd double of a Hopf algebra is a tensor Morita invariant of the Hopf algebra, and it is a useful invariant.

Research Products

• [Journal Article] Schrodinger representations of Drinfel'd doubles of Hopf algebras from the viewpoint of tensor Morita invariants (2013)
  • Author(s): 和久井道久
  • Journal Title: 数理解析研究所講究録 Volume: 1840 Pages: 89-108
  • Peer Reviewed
• [Presentation] 球面構造を用いたホップ代数の多項式不変量の変種 (2012)
  • Author(s): 和久井道久
  • Organizer: 研究集会「可微分写像の特異点とその応用」
  • Place of Presentation: 日本大文理学部
  • Year and Date: 2012-12-10
• [Presentation] Schrodinger representations of Drinfel'd doubles of Hopf algebras from the viewpoint of tensor Morita invariants (2012)
  • Author(s): 和久井道久
  • Organizer: 研究集会「ホップ代数と量子群-応用の可能性」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2012-09-04
• [Presentation] Schrodinger representations of Drinfel’d doubles of Hopf algebras from the viewpoint of tensor Morita invariants (2012)
  • Author(s): 和久井道久
  • Organizer: ホップ代数と量子群---応用の可能性
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] 球面構造を用いたホップ代数の多項式不変量の変種 (2012)
  • Author(s): 和久井道久
  • Organizer: 可微分写像の特異点とその応用
  • Place of Presentation: 日本大学文理学部
• [Presentation] 再考「On Dijkgraaf-Witten invariants of 3-manifolds」 (2011)
  • Author(s): 和久井道久
  • Organizer: 結び目の量子化とそのカテゴリー化
  • Place of Presentation: 早稲田大学(東京都)
  • Year and Date: 2011-08-25
• [Presentation] Tensor Morita invariants of finite-dimensional Hopf algebras associated with the Hopf link (2010)
  • Author(s): 和久井道久
  • Organizer: 研究集会「ホップ代数と量子群」
  • Place of Presentation: 筑波大学
  • Year and Date: 2010-10-18
• [Presentation] Tensor Morita invariants of finite-dimensional Hopf algebras associated with the Hopf link (2010)
  • Author(s): 和久井道久
  • Organizer: ホップ代数と量子群
  • Place of Presentation: 筑波大学
  • Year and Date: 2010-10-18
• [Remarks]
  • URL: http://www2.itc.kansai-u.ac.jp/~wakui/index.html
• [Remarks] 研究紹介
  • URL: http://www2.itc.kansai-u.ac.jp/~wakui/index.html