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A study on pairings

Research Project

Project/Area Number 04640111
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 代数学・幾何学
Research InstitutionFukuoka University

Principal Investigator

ODA Nobuyuki  Fukuoka Univ.prof., 理学部, 教授 (80112283)

Co-Investigator(Kenkyū-buntansha) SUMI T.  Fukuoka, Univ.Assistant, 理学部, 助手 (50258513)
KUROSE T.  Fukuoka, Univ.Lecturer, 理学部, 講師 (30215107)
FUKUSHIMA Y.  Fukuoka, Univ.Asso.prof., 理学部, 助教授 (40099007)
KUROSE H.  Fukuoka, Univ.Asso.prof., 理学部, 助教授 (00161795)
AKIYAMA K.  Fukuoka, Univ.prof., 理学部, 教授 (70078575)
陶山 芳彦  福岡大学, 理学部, 教授 (70028223)
井上 淳  福岡大学, 理学部, 教授 (50078557)
Project Period (FY) 1992 – 1993
Project Status Completed (Fiscal Year 1993)
Budget Amount *help
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1993: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1992: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywordspairing / category / translation plane / quatum group / pluriharmonic / dual connection / divergence / action / ホモトピー / ヒルベルト空間 / 作用素 / ホップ代数 / 移行平面 / 正則写像
Research Abstract

We obtained some properties of pairings in general categories. We studied pairings concerning topologcal spaces, finite groups, quantum groups, pluriharmonic functions, differentiable manifolds, pseudo-Riemannian manifolds.
We determined a class of translation planes of order q^3 admitting a collineation group of order q^3.
For every Hopf **-algebra with a faithful Haar measure, we describe its regular representation as a direct sum of finite dimensional irreducible representations.
Let EPSION be a DFN-space or a complex vector space with the finite open topology, (OMEGA, psi) be a Riemann domain over EPSILON and (lambda^^-, OMEGA^^-, psi^^-) the envelope of holomorphy of (OMEGA, psi). Then any real-valued pluriharmonic function on OMEGA is equal to the real part of a holomorphic function on OMEGA if and only if H^1(OMEGA^^-, R) = 0.
We studied geometly of dual connections (metric-conjugate connections) on pseudo-Riemannian manifolds and he obtained the following result : When a dual connection has constant curvature, we can canonically determine a square-distance-like function which satisfies the generalized Pythagorean theorem.
We consider finiteness obstructions of the total space for a principal fibration. If the fiber is a compact Lie group, we proved that there are many cases that the total space has an equivariant homotopy type of a finite equivariant CW complex under the restriction of the action.

Report

(3 results)
  • 1993 Annual Research Report   Final Research Report Summary
  • 1992 Annual Research Report
  • Research Products

    (23 results)

All Other

All Publications (23 results)

  • [Publications] N.Oda: "Pairings in categories" Publ.Res.Inst.Math.Sci.Kyoto Univ.29. 667-680 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] K.Akiyama: "On the sherk plane" Journal of Geometry. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] H.Kurose: "Extensions of unbounded representations" Mathematische Nachrichten. 155. 257-268 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Y.Fukushima: "Pluriharmonic functions as the real parts of holomorphic functions on a locally convex space" Proceedings of the First Koren-Japanese Colloquium on Finite or Infinite Dimensional Complex. 151-157 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] T.Kurose: "On the divergences of 1-conformally flat statistical manifolds" Tohoku Mathematical Journal. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] T.Kanenobu T.Sumi: "Polynomial invariants of 2-bridge knots through 22 crossings" Mathematics of Computations. 60. 771-778 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] N.Oda: "Pairing in categories" Publ.Res.Inst.Math.Sci.Kyoto Univ.vol.29. 667-680 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] K.Akiyama: "On the sherk plane" Journal of Geometory. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Y.Fukushima: "Pluriharmonic functions as the real parts of holomorphic functions on a locally convex space" Proceedings of the First Korean-Japanese Colloquium on Finite or Infinite Dimensional Complex. 151-157 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] T.Kurose: "ON the divergences of l-conformally flat statistical manifolds" Tohoku Mathematical Journal. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] T.Kanenobu & T.Sumi: "Polynomial invariants of 2-bridge knots through 22 crossings" Mathematics of Computations. vol.60. 771-778 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] N.Oda: "Pairings in categories" publ.Res.Inst.Math.Sci.Kyoto Univ.29. 667-680 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] K.Akiyama: "On the Sherk Plane" Journal of Geometry(to appear).

    • Related Report
      1993 Annual Research Report
  • [Publications] H.Kurose: "Extensions of unbounded representations" Mathematische Nachrichten. 155. 257-268 (1992)

    • Related Report
      1993 Annual Research Report
  • [Publications] Y.Fukushima: "pluriharmonic functions as the real parts of holomorphic functions on a locally convex space" proceedings of the First Koren-Japanese Collo-quium on Finite or Infinite Dimensional Complex Analysis. 151-157 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] T.Kurose: "On the divergences of 1-conformally flat statistical manifolds" Tohoku Mathematical Journal. (to appear).

    • Related Report
      1993 Annual Research Report
  • [Publications] T.Kanenobu T.Sumi: "polynomial invariants of 2-bridge knots through 22 crossings" Mathematics of Computations. 60. 771-778 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] N.Oda: "Pairings and copairings in the category of topological spaces" Publ.RIMS,Kyoto Univ.28. 83-97 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] N.Oda: "Pairings in categories" Publ.RIMS,Kyoto Univ.

    • Related Report
      1992 Annual Research Report
  • [Publications] A.Inoue: "Modular structure of algebras of unbounded operators" Math.Proc.Camb.Phil.Soc.111. 369-386 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] A.Inoue: "Partial O^*-algebras generated by two closed symmetric operators" J.Operator Theory.

    • Related Report
      1992 Annual Research Report
  • [Publications] A.Inoue,H.Kurose,S.Ota: "Extensions of unbounded representation" Math.Nachr.155. 257-268 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] K.Akiyama: "On the Sherk plane" Journal of Geometry.

    • Related Report
      1992 Annual Research Report

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Published: 1992-04-01   Modified: 2016-04-21  

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