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On the construction and classification of the finite geometry

Research Project

Project/Area Number 09640306
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionFukuoka University

Principal Investigator

ODA Nobuyuki (1998)  Fukuoka Univ., Fac.of Science, Prof., 理学部, 教授 (80112283)

秋山 獻之 (1997)  福岡大学, 理学部, 教授 (70078575)

Co-Investigator(Kenkyū-buntansha) AKIYAMA Kenji  Fukuoka Univ., Fac.of Science, Prof., 理学部, 教授 (70078575)
AKITA Toshiyuki  Fukuoka Univ., Fac.of Science, Assistant, 理学部, 助手 (30279252)
KUROSE Takashi  Fukuoka Univ., Fac.of Science, Assoc.Prof., 理学部, 助教授 (30215107)
INOUE Atsushi  Fukuoka Univ., Fac.of Science, Prof., 理学部, 教授 (50078557)
小田 信行  福岡大学, 理学部, 教授 (80112283)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1998: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1997: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywordsgeometry / homotopy / algebra / cohomology / plane / Schur ring / 射影平面 / 共線変換群 / 擬正則 / 積差集合
Research Abstract

Geometrical constructions in homotopy sets were studied. We obtained results on the GAMMA-Whitehead product and the GAMMA-Hopf construction. We introduced the transformation between pairings and copairings and showed its applications. We obtained a formula for the smash product. We obtained a generalization of the Hardie-Jansen product and studied its properties. Dual results are also studied.
For geometrical construction in operator algebras, Tomita-Takesaki theory was studied. We obtained results on unbounded C^*seminorms on *-algebra and standard weights which enable us to develop unbounded Tomita-Takesaki theory.
We constructed explicit examples of surfaces in affine spaces of dimension three and four. We gave a necessary and sufficient condition on surfaces in a three-dimensional affine space to be metric when the surfaces have non-zero constant Gauss-Kronecker curvature.
The cohomology of mapping class groups was studied. We obtained a relation among periodic automorphisms of closed surfaces and the eta-invariant of their mapping tori. We also obtained various vanishing theorems of mod 2 Morita-Mumford classes.
The Schur ring of product type was characterized by the existence of a subgroup of a collineation group. The existence of a Schur ring of produt difference set type is characterized by a finite projective plane of order n with a collineation group of order n(n - 1).

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] N.Oda: "A generalization of the Whitehead product" Math.J.Okayama Univ.to appear.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Oda and T.Shimizu: "Smash product with Γ-Whitehead product and its dual" Far East J.Math.Sci.6(5). 707-726 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Oda and T.Shimizu: "Transformation between pairings" Fukuoka Univ.Sci.Reports. 28. 53-64 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] A.Inoue: "Standard systems for semifinite O-algebras" Proc.Amer.Math.Soc.128. 3303-3312 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Akita: "On the cohomology of Coxeter groups and their finite parabolic subgroups. II" Proc.Sympos.Pure Math.63. 1-5 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Akita: "Euler characteristics of Coxeter groups, PL-triangulations of closed manifolds, and cohomology of subgroups of Artin groups" Journal of the London Mathematical Society. to appear.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Atsushi Inoue: "Tomita-Takesaki Theory in Algebras of Unbounded Operators, Lecture Notes in Mathematics 1699" Springer, 241 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Oda: "A generalization of the Whitehead product" Math.J.Okayama Univ.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Oda and T.Shimizu: "Smash product with GAMMA-Whitehead product and its dual" Far East J.Mach.Sci.6(5). 707-726 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Oda and T.Shimizu: "Transformation between pairings" Fukuoka Univ.Sci.Reports. 28(2). 53-64 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] A.Inoue: "Standard systems for semifinite O^* -algebras" Proc.Amer.Math.Soc.128. 3303-3312 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Akita: "On the cohomology of Coxeter groups and their finite parabolic subgroups.II" Proc.Sympos.Pure Math.63. 1-5 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Akita: "Euler characteristics of Coxeter groups, PL-triangulations of closed manifolds, and cohomology of subgroups of Artin groups" J.London Math.Soc.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] A.Inoue: "Tomita-Takesaki Theory in Algebras of Unbounded Operators" Lecture Notes in Mathematics 1699, Springer. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Oda: "A generalization of the Whitehead product" Math.J.Okayama Univ.to appear

    • Related Report
      1998 Annual Research Report
  • [Publications] N.Oda and T.Shimizu: "Smash product with T-Whitehead product and its dual" Far East J.Math. Sci.6(5). 707-726 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] N.Oda and T.Shimizu: "Transformation between pairings" Fukuoka Univ. Sci. Reparts. 28(2). 53-64 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] N.Oda and T.Shimizu: "Natural maps between some T-suspension spaces and T-loop spaces" Fukuoka Univ. Sci. Reports. 29(1)(to appear). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Akita: "On the cohomology of Coxeter groups and their finite parabo lic subgroups. II" Proc.Sympos.Pure Math.63. 1-5 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Akita: "Euler characteristics of Coxeter groups,PL-triangulations of closed manifolds,and cohomology of subgroups of Artin groups" Journal of the London Mathematical Society. (to appear).

    • Related Report
      1998 Annual Research Report
  • [Publications] Atsushi Inoue: "Tomita-Takesaki Theory in Algebras of Unbounded Operators,Lercture Notes in Mathematics 1699" Springer, 241 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 井上淳, 池田いつ子, 高倉真由美: "Unitary equivalence of unbounded representations of *-algebras" Math.Proc.Camb.Phil.Soc.122. 269-279 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 井上淳, J.P.Antoine, 荻秀和: "Standard generalized vectors for partial O^*-algebras" Ann.Inst.H.Poincare. 67. 223-258 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 井上淳, 荻秀和: "Regular weights on algebras of unbounded operators" J.Math.Soc.Japan. 50. 227-252 (1998)

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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