| Project/Area Number |
10640206
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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 University, faculty of education, professor, 教育学部, 教授 (10093395)
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| Co-Investigator(Kenkyū-buntansha) |
YOKOYAMA Ryouzou Osaka Kyoiku University, faculty of education, professor, 教育学部, 教授 (80124783)
FUJII Masatoshi Osaka Kyoiku University, faculty of education, professor, 教育学部, 教授 (10030462)
CHODA Hisashi Osaka Kyoiku University, faculty of education, professor, 教育学部, 教授 (00030338)
O'UCHI Motoo Osaka Women's University, faculty of science, professor, 理学部, 教授 (70127885)
KAWAKAMI Satoshi Nara University of Education, faculty of education, professor, 教育学部, 教授 (20161284)
竹鼻 宏昭 大阪教育大学, 教育学部, 助教授 (40116166)
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| Project Period (FY) |
1998 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1999: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1998: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | Conjugacy of G-Kernel / group action / Cuntz algebra / Hilbert bimodule / 超有限因子環 / Cuntz-Krieger環 / 群作用の特性類 |
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| Research Abstract |
A homomorphism α from an amenable discrete group G into Out(M)is call G-kernel. Then G-kernels α, β are outer conjugate if there is an automorphism θ of M with α[θ] = [θ]β. Our aim is to classify completely the conjugacy of G-kernel. If G×R acts on commutative von Neumann algebra C, R is ergodic and Q=G/N, then we at first characterize an invariant HィイD4〜ィエD4ィイD13ィエD1(Q×R,C)in algebraic way in terms of HィイD13ィエD1(Q×R,C), HィイD13ィエD1(Q,C)ィイD1RィエD1×ZィイD12ィエD1(Q,HィイD11ィエD1(R,C)), and we obtain two exact sequences.
We consider generalized Cuntz algebra induced by B-Hilbert bimoduleX of finite type. We show that the fixed point algebra with respect to gauge action is simple if and only if B is X-aperiodic. The definition of B is X-aperidodic is a generalization that transition matrix is aperiodic. Let U be an operator on X. If a certain automorphism αィイD2UィエD2 on generalized Cuntz algebra is inner, then it is trivial on a relative commutant of the fixed point algebra. Applying this to Cuntz-Krieger algebra, the automorphisms αィイD2UィエD2 is inner or weakly inner with canonical state ψ if and only if the operator U is a type of coboundary.
And we show that we give a tensor product formulae of characteristic invariant for actions of an group. In the case of a certain factor of type III, we can compute explicitly the formulae. Let α,β be two actions which commute mutually. We give a formulae to give characteristic invariant for an extended action α on the partial crossed product by β. we can show explicitly the formulae for a certain factor of type III in the case that the group is abelian,
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