On the research of a geometric realization of subfactors and its applications
Project/Area Number |
22540234
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Global analysis
|
Research Institution | Rikkyo University |
Principal Investigator |
SATO Nobuya 立教大学, 理学部, 准教授 (60305662)
|
Project Period (FY) |
2010-10-20 – 2014-03-31
|
Project Status |
Completed (Fiscal Year 2013)
|
Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
|
Keywords | 部分因子環 / paragroup / Q-system / コホモロジー群 / 幾何学的表現 / Weyl群 / フロベニウス代数 / 幾何学的実現 / 再生核ヒルベルト空間 / similarity orbit / ループ群 / 3次元Chern-Simons理論 / subfactor planar algebra / 3次元多様体の位相不変量 / D2n-線形スケイン / subfactorの幾何学的表現 / Borel-Weil-Bottの定理 / Beltita-Gale / Cuntz環 / subfactor |
Research Abstract |
During the period of research, I obtained the following three results. (1) I constructed a geometric representation of the unitary group of a type II_1 factor with a subfactor.(2) For a Q-system associated with a subfactor, I defined the cohomology groups up to degree three via the method of deviation.(3) I constructed a new example of the increasing sequence of Weyl groups defined by Argerami-Stojanoff and showed that in the most of cases the Weyl groups are trivial.
|
Report
(5 results)
Research Products
(3 results)