Algebraic structures and analysis in tensor categories and quantum groupoids
| Project/Area Number |
15540196
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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 | Ibaraki University |
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Principal Investigator |
YAMAGAMI Shigeru Ibaraki University, College of Science, Professor, 理学部, 教授 (90175654)
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| Co-Investigator(Kenkyū-buntansha) |
OSHIMA Hideaki Ibaraki University, College of Science, Professor, 理学部, 教授 (70047372)
MASUOKA Akira Tsukuba University, Graduate School of Pure and Applied Sicences, Associate Professor, 数理物質科学研究科, 助教授 (50229366)
YAMANOUCHI Takehiko Hokkaido University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (30241293)
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| Project Period (FY) |
2003 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2005: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2004: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2003: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Keywords | tensor category / Frobenius algebra / fiber functor / 量子群 / Temperley-Lieb圏 / 量子亜群 / ホップ代数 |
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| Research Abstract |
1
An important class of tensor categories arises as representation categories of finite-dimensional Hopf algebras. We here have studied its significance in the framework of tensor categories, which is boiled down to the notion of Frobenius algebra in tensor categories.
A duality on quantum symmetry is then formulated in terms of Frobenius algebra bimodules in a tensor categories. The main result is published in Fields Institute Commun.
2
We have investigated Temperley-Lieb categories based on Kauffman's presentation and clarified how all the known structural results follow from elementary manipulations of planar strings.
3
As applications of the above mentioned geometrical analysis, we have tried to determine fiber functors on Temperley-Lieb categories.
The result is that fiber functors are determined by non-degenerate bilinear forms up to the similarity equivalence, which turns out to be related with the known old theorems. If we restrict ourselves to the case of unitary fiber functors, we can rewrite the conditions in terms of spectral data of kernel matrices, which recovers the known theory on representations of the associaited compact quatum groups.
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Report
(4 results)
Research Products
(15 results)
