2003 Fiscal Year Final Research Report Summary
G-kernel of amenable discrete groups on AFD factors of type III
| Project/Area Number |
14540206
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Osaka Kyoiku University |
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Principal Investigator |
KATAYAMA Yoshikazu Osaka Kyoiku Univ., Department of Education, Professor, 教育学部, 教授 (10093395)
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| 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)
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| Project Period (FY) |
2002 – 2003
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| Keywords | G-kernel / outer conjugate / amenable discrete group / factor of type III |
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| 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.
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Research Products
(10 results)
