2004 Fiscal Year Final Research Report Summary
Reseach of non commutative geometry
| Project/Area Number |
14540092
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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 |
Geometry
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| Research Institution | TOKYO UNIVERSITY OF SCIENCE |
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Principal Investigator |
OMORI Hideki Tokyo Univ.of Science, Science & Technology, Prof., 理工学部, 教授 (20087018)
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| Co-Investigator(Kenkyū-buntansha) |
YOSHIOKA Akira Tokyo Univ.of Science, Science, Prof., 理工学部, 教授 (40200935)
KOBAYASHI Reido Tokyo Univ.of Science, Science & Technology, Prof., 理工学部, 教授 (70120186)
KOBAYASHI Takao Tokyo Univ.of Science, Science & Technology, Prof., 理工学部, 教授 (90178319)
TANAKA Makiko Tokyo Univ.of Science, Science & Technology, Ass.Prof., 理工学部, 助教授 (20255623)
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| Project Period (FY) |
2002 – 2004
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| Keywords | Non-commutative Geometry / Star-product / Deformation quantization |
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| Research Abstract |
In the transcendently extended Weyl algebra, there was no systematic theory of intertwiners. This research attempt to construct a systematic theory for these. Here is the summary of facts, uncovered by the research :
1)Existence of multi-valued elements
This is observed as monodromy phenomena for the parallel translation by infinitesimal intertwiners. That is, even though the parameter of expression came back to the starting point, the parallelly translated element did not come back to the starting point.
2)Group-like object which does not form a point set
This is viewd as a model regarded as a non-trivial double covering group of a "simply connected" Lie group.
In the traditional mathematics, such an object is logically impossible. However, it is permitted to exist, because of the existence of multi-valued elements.
3)Manifolds patched by multi-valued coordinate transformations
Multi-valued functions are familiar in classical mathematics. However, there was no notion of manifolds, which are understood as a patchwork of local coordnate neighborhoods by multivalued coordinate transformations. Such notions are required to understand the phenomena mentioned above.
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