Quantum analysis in tensor categories and their free products
| Project/Area Number |
18540201
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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, 理学部, 教授 (90175654)
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| Co-Investigator(Kenkyū-buntansha) |
日合 文雄 東北大学, 情報科学研究科, 教授 (30092571)
泉 正己 京都大学, 理学研究科, 教授 (80232362)
大嶋 秀明 茨城大学, 理学部, 教授 (70047372)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,020,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥720,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | テンソル圏 / 自由積 / 平面代数 / 作用素環 / 量子代数 / 遷移確率 / 面代数 / 双加群 / 分岐則代数 |
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| Research Abstract |
Traditionally, scientific symmetry is described in terms of a mathematical notion called group. As a consequence of recent studies on symmetry in the field of mathematical physics, we are faced with a new phase of symmetry, which is out of coverage in the ordinary group notion and referred to as quantum symmetry. After closer investigations on the subject, the relevant notion in describing quantum symmetry turned out to be that of tensor category.
In this research project, we focus on planar diagrams and have revealed that their matrix representations are in one-to-one correspondence with singly generated tensor categories.
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Report
(6 results)
Research Products
(11 results)
