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Noncommutative Geometry and groupoid

Research Project

Project/Area Number 18540093
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionKeio University

Principal Investigator

MIYAZAKI Naoya  Keio University, 経済学部, 教授 (50315826)

Project Period (FY) 2006 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥4,150,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥750,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
Keywords変形量子化 / 指数定理 / 非可換幾何学 / 亜群 / 量子化 / ジャーブ / 非可換幾何 / twisted vectorial bundle / gerbe / 変形理論 / index theorem / 熱核 / K-理論 / noncommutative geometr / deformation quantization / star product / groupoid / automorphism group / svmplectic diffeomorphism / noncommutative geometry
Research Abstract

We studied noncommutative geometry, cyclic theory, K-theory, Dirac operator on a groupoid. It is very important to resolve the fundamental problems and extension of index theory to noncommutative theory. On the other hand, we also studied nonformal deformation quantization and transcendental elements which appear nonformal deformation quantization, because they are regarded as representative of noncommutative phenomena.

Report

(6 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report   Self-evaluation Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (15 results)

All 2009 2008 2007 2006 Other

All Journal Article (13 results) (of which Peer Reviewed: 8 results) Presentation (1 results) Remarks (1 results)

  • [Journal Article] Remarks on deformation quantization2009

    • Author(s)
      宮崎直哉
    • Journal Title

      Geometric Mechanics(RIMS, Kyoto University)

      Pages: 1-3

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Characteristic classes relating to quantizat2008

    • Author(s)
      Naoya Miyazaki
    • Journal Title

      in京都大学数理解析研究所講究録 1576

      Pages: 67-81

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Characteristic classes relating to quantizaton2008

    • Author(s)
      Miyazaki. N
    • Journal Title

      京都大学数理解析研究所講究録1576

      Pages: 67-81

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Characteristic classes relating to quantizaton2008

    • Author(s)
      宮崎直哉
    • Journal Title

      京都大学数理解析研究所講究録 1576

      Pages: 67-81

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Lifts of symplectic diffeomorphisms as automorphisms of a Weyl algebra bundle with Fedosov connection2007

    • Author(s)
      Naoya Miyazaki
    • Journal Title

      International Journal of Geometric Methods in Modern Physics 4

      Pages: 533-546

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Examples of Groupoid, in Proceedings of the international2007

    • Author(s)
      Naoya Miyazaki
    • Journal Title

      Sendai-Beijing joint workshop

      Pages: 97-108

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Lie group structure for automorphisms of a contact Weyl manifold in From Geometry to Quantum Mechanics2007

    • Author(s)
      Naoya Miyazaki
    • Journal Title

      Progress in Mathemastics 252(Birkhauser)

      Pages: 25-44

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Lie group structure for automorphisms of a Contact Weyl manifold2007

    • Author(s)
      Miyazaki. N
    • Journal Title

      Progress in Mathematics 252(Birkhauser)

      Pages: 25-44

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Examples of groupoid2007

    • Author(s)
      Miyazaki. N
    • Journal Title

      in Noncommutative geometry and Physics

      Pages: 97-108

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Lifts of symplectic diffeomorphisms as automorphisms of a Weyl algebrabundle with Fedosov connection2007

    • Author(s)
      Naoya Miyazaki
    • Journal Title

      International Journal of Geometric Methods in Modern Physics 4

      Pages: 533-546

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Lie group structure for Automorphisms of a contact Weyl manifold2007

    • Author(s)
      Naoya Miyazaki
    • Journal Title

      Progress in Mathematics 252

      Pages: 25-44

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On the integrability of deformation quantized Toda lattice2006

    • Author(s)
      Naoya Miyazaki
    • Journal Title

      Acta Appl. Mathematecae 92

      Pages: 21-36

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the integrability of deformation quantized Toda lattice2006

    • Author(s)
      Naoya Miyazaki
    • Journal Title

      Acta Applicandae Mathematicae 92

      Pages: 21-36

    • Related Report
      2006 Annual Research Report
  • [Presentation] Remarks on deformation quantization2009

    • Author(s)
      宮崎直哉
    • Organizer
      京都大学数理解析研究所共同研究会「幾何学的力学系」
    • Place of Presentation
      京都大学において
    • Year and Date
      2009-12-21
    • Related Report
      2009 Final Research Report
  • [Remarks] 2006年、2008年に慶應義塾大学日吉キャンパスにおいて、・非可換幾何学と数理物理学2006・非可換幾何学と数理物理学2008を開催し若手並びに中堅の研究者の交流、情報交換を行った

    • Related Report
      2009 Final Research Report

URL: 

Published: 2006-04-01   Modified: 2016-04-21  

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