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2003 Fiscal Year Final Research Report Summary

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
KeywordsG-kernel / outer conjugate / amenable discrete group / factor of type III
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.

  • Research Products

    (10 results)

All Other

All Publications (10 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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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

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Published: 2005-04-19  

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