Research of operator algebraic quantum groups

• Project/Area Number: 21740112
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: Hokkaido University (2011); Tokyo University of Science (2009-2010)
• Principal Investigator: TOMATSU Reiji 北海道大学, 大学院・理学院研究院, 准教授 (70447366)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: von Neumann環 / 量子群 / 作用 / Rohlin性 / flow / Kac環 / 自己同型 / 連結単純lie群

Research Abstract

I jointly work with A. Skalski and F. Uwe on a compact quantum group whose Haar state admits a non-trivial square root. Also, with Toshihiko Masuda(Kyushu university), I studied the action of the additive real group on a von Neumann algebra. We especially obtain a classification of Rohlin flows up to strong cocycle conjugacy.

Research Products

• [Journal Article] On Square Roots of the Haar State on Compact Quantum Groups (2012)
  • Author(s): U. Franz, A. Skalski, R. Tomatsu
  • Journal Title: the Journal of Pure and Applied Algebra Volume: Volume216, Issue10 Pages: 2079-2093
• [Journal Article] On square roots of the Haar state on comapact quantum groups (2012)
  • Author(s): U.Franz, A.Skalski, R.Tomatsu
  • Journal Title: Journal of Pure and Applied Algebra Volume: (掲載確定) Issue: 10 Pages: 2079-2093
  • DOI: 10.1016/j.jpaa.2012.01.020
  • Peer Reviewed
• [Journal Article] Classification of minimal actions of a compact Kac algebra with amenable dual on injective factors of type III (2010)
  • Author(s): 戸松玲治、増田俊彦
  • Journal Title: Journal of Funcional Analysis 258 Pages: 1965-2025
  • Peer Reviewed
• [Journal Article] A Galois correspondence for compact quantum group actions (2009)
  • Author(s): 戸松玲治
  • Journal Title: Journal fur die reine und anguewandte Mathema-tik 633 Pages: 165-182
  • Peer Reviewed
• [Journal Article] Approximate innerness and central triviality of endomorphisms (2009)
  • Author(s): 戸松玲治、増田俊彦
  • Journal Title: Advances in Mathematics 220 Pages: 1075-1134
  • Peer Reviewed
• [Presentation] Classification of actions of discrete amenable Kac algebras on von Neumann algebras (2012)
  • Author(s): R. Tomatsu
  • Organizer: Conference on von Neumann algebras and Related Topics, RIMS
  • Place of Presentation: Kyoto University,(Kyoto city)
  • Year and Date: 2012-01-12
• [Presentation] Classification of actions of amenable discrete Kac algebras on injective factors (2012)
  • Author(s): 戸松玲治
  • Organizer: Conference on von Neumanna algebras and relatea topics
  • Place of Presentation: 京都大学(京都市)(招待講演)
  • Year and Date: 2012-01-12
• [Presentation] フォンノイマン環への群・量子群作用の分類II,IV (2011)
  • Author(s): 戸松玲治
  • Organizer: RIMS共同研究 作用素環の対称性の研究
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] Kac型従順離散量子群の従順因子環への作用の分類 (2010)
  • Author(s): R. Tomatsu
  • Organizer: 日本数学会
  • Place of Presentation: 名古屋大学(名古屋市)
  • Year and Date: 2010-09-24
• [Presentation] Kac型従順離散量子群の従順因子環への作用の分類 (2010)
  • Author(s): 戸松玲治
  • Organizer: 2010日本数学会秋季総合分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-24
• [Presentation] Classification of actions of discrete amenable Kac algebras on von Neumann algebras (2010)
  • Author(s): R. Tomatsu
  • Organizer: 実函数論関数解析学合同シンポジウム
  • Place of Presentation: 東京理科大学野田キャンパス(野田市)
  • Year and Date: 2010-08-02
• [Presentation] 従順離散カッツ環の単射的因子環への作用の分類 (2010)
  • Author(s): 戸松玲治
  • Organizer: 実関数論関数解析合同シンポジウム
  • Place of Presentation: 東京理科大学野田キャンパス
  • Year and Date: 2010-08-02
• [Presentation] Classification of actions of discrete amenable Kac algebras on von Neumann algebras (2009)
  • Author(s): R. Tomatsu
  • Organizer: Non-commutative Harmonic Analysis with Applications to Probability
  • Place of Presentation: Bedlewo(Poland)
  • Year and Date: 2009-08-21
• [Presentation] Classification of actions of a discrete amenable Kac algebra on amenable von Neumann factors (2009)
  • Author(s): 戸松玲治
  • Organizer: 12^<th> workshop Non-commutative harmonic analysis
  • Place of Presentation: The mathematical research and conference center, Poland
  • Year and Date: 2009-08-21
• [Remarks]
  • URL: http://www.math.sci.hokudai.ac.jp/~tomatsu/index.html
• [Remarks]
  • URL: http://www.math.sci.hokudai.ac.jp/~tomatsu/index.html
• [Remarks]
  • URL: http://www.ma.noda.tus.ac.jp/u/rto/index.html