On diagram algebras

• Project/Area Number: 22540026
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: University of the Ryukyus
• Principal Investigator: KOSUDA Masasi 琉球大学, 理学部, 准教授 (40291554)
• Project Period (FY): 2010-10-20 – 2014-03-31
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); 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: ダイアグラム代数 / Murphy元 / Motzkin代数 / Khovanov代数 / cell表現 / Diagram代数 / Cell表現 / Murphy作用素 / Party代数 / Partition代数 / Cell代数 / Seminormal Form

Research Abstract

This research was intended to "Categorify" the q-walled Brauer algebra. We found that although this algebra is very complicated, the application of it would be very limited. So we have changed the research object slightly and began to study Khovanov's diagram algebra and Motzkin algebra. We have not yet succeeded the "Categorification" of Khovanov's algebra. However we have succeeded to define the defining relation go the Motzkin algebra. Khovanov algebra will become an important tool which binds topological objects and algebraic objects.

Research Products

• [Journal Article] Party代数のcell構造 (2013)
  • Author(s): 小須田雅
  • Journal Title: 数理解析研究所講究録
• [Journal Article] Diagram 代数の cell構造 (2013)
  • Author(s): 小須田雅
  • Journal Title: 数理解析研究所講究録 Volume: 未定
• [Presentation] Party代数のcell構造 (2012)
  • Author(s): 小須田雅
  • Organizer: ホップ代数と量子群
  • Place of Presentation: 京都
• [Presentation] Party代数のcell構造 (2012)
  • Author(s): 小須田雅
  • Organizer: 数理解析研究所研究集会「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
• [Presentation] タングルの不変量と表現 (2011)
  • Author(s): 小須田雅
  • Organizer: 2011琉球結び目セミナー
  • Place of Presentation: 那覇市伝統工芸館会議室
  • Year and Date: 2011-09-06
• [Presentation] タングルの不変量と表現 (2011)
  • Author(s): 小須田雅
  • Organizer: 琉球結び目セミナー
  • Place of Presentation: 沖縄
• [Remarks]
  • URL: http://www.math.u-ryukyu.ac.jp/~kosuda/
• [Remarks]
  • URL: http://www.researchgate.net/profile/Masashi_Kosuda