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On the research of a geometric realization of subfactors and its applications

Research Project

Project/Area Number 22540234
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionRikkyo University

Principal Investigator

SATO Nobuya  立教大学, 理学部, 准教授 (60305662)

Project Period (FY) 2010-10-20 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords部分因子環 / paragroup / Q-system / コホモロジー群 / 幾何学的表現 / Weyl群 / フロベニウス代数 / 幾何学的実現 / 再生核ヒルベルト空間 / similarity orbit / ループ群 / 3次元Chern-Simons理論 / subfactor planar algebra / 3次元多様体の位相不変量 / D2n-線形スケイン / subfactorの幾何学的表現 / Borel-Weil-Bottの定理 / Beltita-Gale / Cuntz環 / subfactor
Research Abstract

During the period of research, I obtained the following three results.
(1) I constructed a geometric representation of the unitary group of a type II_1 factor with a subfactor.(2) For a Q-system associated with a subfactor, I defined the cohomology groups up to degree three via the method of deviation.(3) I constructed a new example of the increasing sequence of Weyl groups defined by Argerami-Stojanoff and showed that in the most of cases the Weyl groups are trivial.

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (3 results)

All 2010

All Journal Article (1 results) Presentation (2 results)

  • [Journal Article] An invitation to V.F.R.Jones'planar algebras2010

    • Author(s)
      Nobuya SATO
    • Journal Title

      数理解析研究所講究録

      Volume: 第1716巻 Pages: 64-83

    • Related Report
      2013 Final Research Report
  • [Presentation] A representation of planar operads-V.F.R.Jones' theory of planar algebras-2010

    • Author(s)
      Nobuya Sato
    • Organizer
      Workshop on Noncommutative Geometric Approach to the Index Theory for Singular Spaces
    • Place of Presentation
      関西セミナーハウス
    • Year and Date
      2010-10-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] An introduction to the planar algebras2010

    • Author(s)
      佐藤信哉
    • Organizer
      Intelligence of Low-dimensional Topology
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-06-03
    • Related Report
      2013 Final Research Report

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Published: 2010-11-30   Modified: 2019-07-29  

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