2009 Fiscal Year Final Research Report
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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| Project Period (FY) |
2006 – 2009
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| Keywords | テンソル圏 / 自由積 |
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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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