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Study of quantum group actions on von Neumann algebras

Research Project

Project/Area Number 24740095
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Global analysis
Research InstitutionHokkaido University

Principal Investigator

TOMATSU Reiji  北海道大学, 理学(系)研究科(研究院), 准教授 (70447366)

Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords作用素環 / von Neumann環 / C*環 / 量子群 / Haagerup property / von Neumann algebra / flow / Rohlin性 / 無限テンソル積作用 / 量子旗多様体 / 誘導作用
Outline of Final Research Achievements

My main research results are ``Analysis of infinite tensor product type actions",``Formulation of Haagerup approximation property for arbitrary von Neumann algebras" and ``Study of Haagerup approximation property of von Neumann algebra by bimodule approach". I showed that any infinite tensor product type action of a q-deformed quantum group is actually induced from its maximal torus. I formulated Haagerup approximation property by using theory of completely positive operators on standard Hilbert spaces of von Neumann algebras. By bimodule approach, I succeeded in strengthening some results obtained before.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (6 results)

All 2015 2013 Other

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (4 results) (of which Invited: 2 results) Remarks (1 results)

  • [Journal Article] Idempotent states on compact quantum groups and their classification on Uq(2), SUq(2), and SOq(3)2013

    • Author(s)
      U. Franz, A. Skalski, R. Tomatsu
    • Journal Title

      J. Noncommut. Geom.

      Volume: 7 Issue: 1 Pages: 221-254

    • DOI

      10.4171/jncg/115

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Haagerup approximation property for locally compact quantum groups2015

    • Author(s)
      戸松玲治
    • Organizer
      テニュアトラックミニ研究集会
    • Place of Presentation
      お茶の水女子大学(東京都文京区)
    • Year and Date
      2015-03-26
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Von Neumann環上のRohlin flowの分類について

    • Author(s)
      戸松玲治
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      九州大学 (福岡市)
    • Related Report
      2012 Research-status Report
  • [Presentation] Rohlin flows on von Neumann algebras

    • Author(s)
      戸松玲治
    • Organizer
      RIMS研究集会
    • Place of Presentation
      京都大学(京都市)
    • Related Report
      2012 Research-status Report
  • [Presentation] Von Neumann環への群・量子群作用の分類問題

    • Author(s)
      戸松玲治
    • Organizer
      日本数学会年会
    • Place of Presentation
      京都大学(京都市)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Remarks] 戸松 玲治

    • URL

      http://www.math.sci.hokudai.ac.jp/~tomatsu/index.html

    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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