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G-kernel of amenable discrete groups on AFD factors of type III

Research Project

Project/Area Number 14540206
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

KATAYAMA Yoshikazu  Osaka Kyoiku Univ., Department of Education, Professor, 教育学部, 教授 (10093395)

Co-Investigator(Kenkyū-buntansha) KAWAKAMI Satoshi  Nara University of Education, Department of Education, Professor, 教育学部, 教授 (20161284)
FUJII Masatoshi  Osaka Kyoiku Univ., Department of Education, Professor, 教育学部, 教授 (10030462)
CHODA Hisashi  Osaka Kyoiku Univ., Department of Education, Professor, 教育学部, 教授 (00030338)
OUCHI Motoo  Osaka Women's Univ., School of Science, Professor, 理学部, 教授 (70127885)
Project Period (FY) 2002 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 2003: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2002: ¥1,300,000 (Direct Cost: ¥1,300,000)
KeywordsG-kernel / outer conjugate / amenable discrete group / factor of type III / 外部共役同値類 / III形因子環
Research Abstract

ABSTRACT. To each factor M, we associate an invariant Ob_m(M) to be called the intrinsic modular abstruction as a cohomological invariant which lives in the "third" cohomology group :
H^<out>_<α,S>(Out(M)×R,H^1_θ(R,U(C),U(C))
where {C,R,θ} is the flow of weights on M. If α is an outer action of a countable discrete group G on M, then its modulus mod(α) ∈ Hom(G, Aut_θ(C)), N = α^<-1>(Cnt_r(M)) and the pull back
Ob_m(α) = α^*(Ob_m(M)) ∈ H^<out>_<α,S>(G×R,N,U(C))
to be called the modular obstruction of α are invariants of the outer conjugacy class of the outer action α.
We prove that if the factor M is approximately finite dimensional and G is amenable, then the invariants uniquely determine the outer conjugacy class of α and the every invariant occurs as the in variant of an outer action α a of G on M.

Report

(3 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • Research Products

    (22 results)

All Other

All Publications (22 results)

  • [Publications] Y.Katayama, M.Takesaki: "Outer Actions of a Discrete Amenable Group on Approximately Finite dimensional Factors I, General theory"Contemporary Mathematics. (To appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Katayama, M.Takesaki: "Outer actions of countable discrete amenable group on AFDfactor"Contemporary Mathematics. 335. 163-171 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.Fujii, Y.O.Kim, Y.Seo: "Further extensions of Wielandt type Heintz-Kato-Furuta inequalities via Furuta inequality"Archives Inequal.Appl.. 1. 275-283 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.Fujii, Y.O.Kim: "A characterization of chaotic order by Furuta type operator inequalities via operator convexity"J.Nonlinear Convex Anal.. 4・2. 215-222 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.O'uchi: "Coring structures associated with multiplicative unitary operators on Hilbert C^*-modules"Far East Journal of Mathematical Sciences. 11・2. 121-136 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Katayama, M.Takesaki: "Outer Actions of a Discrete Amenable Group on Approximately Finite dimensional Factors I, General theory"Contemporary Math.. (To appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Katayama, M.Takesaki: "Outer actions of countable discrete amenable group on AFD factor"Contemporary Mathematics. 335. 163-171 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.Fujii, Y.O.Kim, Y.Seo: "Further extensions of Wielandt type Heinz-Kato-Furuta inequalities via Furuta inequality"Archives Inequal.Appl.. vol.1. 275-283 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.Fujii, Y.O.Kim: "A characterization of chaotic order by Furuta type operator inequalities via operator convexity"J.Nonlinear Convex Anal.. vol.4, No.2. 215-222 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.O'uchi: "Coring structures associated with multiplicative unitary operators on Hilbert C^*-modules."Far East Journal of Mathematical Sciences. Vol.11, NO.2. 121-136 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Katayama, M.Takesaki: "Outer actions of countable discrete amenable group on AFD factor"Contemporary Mathematics. 335. 163-171 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Katayama, M.Takesaki: "Outer Actions of a Discrete Amenable Group on Approximately Finite dimensional Factors I, General theory"Contemporary Mathematics. (To appear).

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Fujii, Y.O.Kim, Y.Seo: "Further extensions of Wielandt type Heinz-Kato-Furuta inequalities via Furuta inequality"Archives Inequal.Appl.. 1. 275-283 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Fujii, Y.O.Kim: "A characterization of chaotic order by Furuta type operator inequalities via operator convexity"J.Nonlinear Convex Anal.. 4・2. 215-222 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Fujii, S.H.Lee, Y.Seo: "Reverse inequalities on chaotically geometric mean via Specht ratio"Math.Inequal.Appl.. 6・3. 509-519 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.O'uchi: "Coring structures associated with multiplicative unitary operators on Hilbert C^*-modules"Far East Journal of Mathematical Sciences. 11・2. 121-136 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Yukako Miwa, Yoshikazu Katayama: "Characteristic invariant of tensor product actions and actions on crossed products"J. Aust. Math. Soc.. 73. 357-376 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Fuijii, E.Kamei R.Nakamoto: "On a question of Furuta on chaotic order"Linear Algebra and its Applications. 341. 119-127 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] J.I.Fujii, M.Fujii: "Kolmogorov's complexity for positive definite matrices"Linear Algebra and its Applications. 341. 171-180 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Fujii, Y.Seo, M.Tominaga: "Golden-Thompson type inequality related to a geometric mean via Specht's ratio"Mathematical Inequalities and Applications. 5-3. 573-582 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.O'uchi: "Pseudo-multiplicative unitaries associated with inclusions of finite-dimensional C^*-algebras"Linear Algebra and its Applications. 341. 201-218 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.O'uchi: "Pentagonal equations for operators associated with inclusions of C^*-algebras"Scientiae Mathematicae Japonicae. 56. 71-94 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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