| Project/Area Number |
09304017
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| Research Category |
Grant-in-Aid for Scientific Research (A).
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
解析学
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| Research Institution | KYUSHU UNIVERSITY |
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Principal Investigator |
KOSAKI Hideki Faculty of Hathematicst.KYUSHU UNIVERSITY Prof., 大学院・数理学研究院, 教授 (20186612)
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| Co-Investigator(Kenkyū-buntansha) |
HAMACHI Toshihiro Faculty of Mathematics KYUSHU UNIVERSITY Prof., 大学院・数理学研究院, 教授 (20037253)
KAWAHIGASHI Yasuyuki Graduate School of Mathomatical Sciemcasi KYUSHU UNIVERSITY Prof., 大学院・数理科学研究科, 教授 (90214684)
IZUMI Masaki Faculty of Sciemce KYUSHU UNIVERSITY Assoc.Prof., 大学院・理学研究科, 助教授 (80232362)
WATATANI Yasuo Faculty of Mathematies KYUSHU UNIVERSITY Prof., 大学院・数理学研究院, 教授 (00175077)
YAHAGAMI Shigeru Faculty of Sciemce KYUSHU UNIVERSITY Prof., 理学部, 教授 (90175654)
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| Project Period (FY) |
1997 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥15,800,000 (Direct Cost: ¥15,800,000)
Fiscal Year 2000: ¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 1999: ¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 1998: ¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 1997: ¥5,000,000 (Direct Cost: ¥5,000,000)
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| Keywords | fusion algebra / Jones index / Kac algebra / Rohlin property / tensor category / Longo-Rehren subfactor / factor / bimedule / エルゴード変換 / 作用素平均 / 部分因子環 / ループ群 / Jones指数理論 / Longo-Rehren対 / C^*環分類 / 作用業平均 / テント写像 / Chacon変換 / 最小作用 / 位相不重量 / 指数理論 / 記号力学元 / セクター理論 / 中間部分因子環 / III_0型因子環 / C^*部分環 |
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| Research Abstract |
There is an active group of researchers of the Jones index theory and related subfactor analysis in our country. Main members in this group studied these subject matters from a variety of different viewpoints such as Ocneanu theory, representations of loop groups, bimodules, structure ananysis on type III factors, ergodic theory, and tensor category. Three conferences were held by support of the current funding. Although a wide variety of subjects in operator theory and operator algebras was investigated by the members in the duration of the current funding, main achievements on the proposed subject are as follows : (i) Longo-Rehren subfactors (closely releted to the notion of a quantum double) and the fusion rule of relevant bimodules were clarified. (ii) A certain deformation theory for Kac algebras via various cocycles was established based on subfactor analysis, and it now becomes possible to classify low-dimensional Kac algebras. (iii) Many "subfactor versions" of structure analysis of type III factors and the notion of orbit equivalence were obtained, and structure of subfactors in type III_0 factors became quite transparent. (iv) The notion of (strong) amenability (required for classification of subfactors) was clarified in many settings such as fusion algebras and tensor categories. (v) Many realizations of Cuntz-Krieger type C^*-algebras were found via bimodule approach, and some new knowledge was added to the understanding of these algebras. (vi) The (non-commutative) Rohlin property for C^*-algebras was successfully formulated, and consequently study on automorphisms of AF and AT algebras has advanced considerably.
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