2000 Fiscal Year Final Research Report Summary
| 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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| Keywords | fusion algebra / Jones index / Kac algebra / Rohlin property / tensor category / Longo-Rehren subfactor / factor / bimedule |
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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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