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2002 Fiscal Year Final Research Report Summary

Study of Poisson geometry and its application

Research Project

Project/Area Number 12440022
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

MAEDA Yoshiaki  Keio University, Dept. of Mathematics, Professor, 理工学部, 教授 (40101076)

Co-Investigator(Kenkyū-buntansha) ICHII Ippei  Keio University, Dept. of Mathematics, Professor, 理工学部, 助教授 (90051929)
TANI Atsushi  Keio University, Dept. of Mathematics, Professor, 理工学部, 教授 (90118969)
KIKUCHI Norio  Keio University, Dept. of Mathematics, Professor, 理工学部, 教授 (80090041)
KAMETANI Yokio  Keio University, Dept. of Mathematics, Assistant Professor, 理工学部, 講師 (70253581)
MORIYOSHI Hitoshi  Keio University, Dept. of Mathematics, Associate Professor, 理工学部, 助教授 (00239708)
Project Period (FY) 2000 – 2002
Keywordsdeformation quantizations / groupoids / Index theorem / D-brane / Hochshields cohomology
Research Abstract

Poisson Geometry, which is the extended notion of symplectic geometry, is now developing quite recently. However, this research fields is not common in Japan, while this research field is much developing in Europe and the United State. In our Study, we have a mission to develop this research fields in Japan, and to coorporate with the researchers who are working on this fields in Europe and the Unites States. The first our development is to study the convergence problems on deformation quantizations. For the case of formal deformations, M. Kontsevich has given a pretty result. It is important problem to study the convergence for the deformation quantizations. Through our research, we found the totally different feature for the convergence of the deformation quantizations, and propose a new geometric objects on gerbes. We will extend our research on the convergence of the deformation quantization as a future task. By this grant, we have two major international symposia in 2001 and 2002, which has noncommutative geometry and D-brane as main Topics. We could have many visitors from abroad and also from domestic research institutes. We have published a proceedings for our research developments. Maeda has been invited to the Poisson 2002 international conference at Lisbon and gave a talk on this problem, which was very interesting for the participants. We have also visited various meetings in Japan and outside of Japan to make strong activities. As a results, we could have a international research groups on noncommutative geometry, which is able to develop the research.

  • Research Products

    (13 results)

All Other

All Publications (13 results)

  • [Publications] 前田 吉昭: "Convengent star product algebras on ax+b"Letters in Mathematical Physics. (2002年度出版予定).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 前田 吉昭: "Strange Phenomena related to ordering problems in quantizations"Journal of Lie Theory. (2002年度出版予定).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 前田 吉昭: "On a construction of a good parametrix for the Pauli equation by Hamiltonian path-integral method ---an application of superanalysis"Japanese Journal of Mathematics. (2002年度出版予定).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 前田 吉昭: "Convert star product on Preehet linear Poisson algebra of Heisenberg type"Contempolary of Mathematics. 288. 391-395 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 前田 吉昭: "Star exponential functions for quadratic forms and polar elements"Contempolary of Mathematics. 315. 25-38 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 前田 吉昭: "Smooth^* -algebras"Progress of Theoretical Physics. 144. 54-78 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 前田 吉昭: "変型量子化入門"東京大学大学院数理科学研究科. 178 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Yoshiaki Maeda: "Convergent star product algebran on axtb"Letters in Mathematical Physics. to appear. (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yoshiaki Maeda: "Strange Phenomena related to ordering problems in quantizations"Journal of Lie Theory. To appear. (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yoshiaki Maeda: "On a constructions of a good parametrix for the Pauli equation by Hamiltonion path-integral method an application of Super analysis"Japanese Journal of Mathematics. to appear. (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yoshiaki Maeda: "Convert Star product on frechet linear Poisson algebra of Heisenberg type"Contemporary of Mathematics. 288. 391-395 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yoshiaki Maeda: "Star exponential functions for quadratic forms and polar elements"Contemporary of Mathematics. 315. 25-38 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yoshiaki Maeda: "Smooth^*-algebras"Progress of Theoretical Physics. 144. 54-78 (2001)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2004-04-14  

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