2006 Fiscal Year Final Research Report Summary
Cayley algebra and Grassmann geometry
| Project/Area Number |
16540055
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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 Agriculture and Technology |
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Principal Investigator |
MASHIMO Katsuya Tokyo University of Agriculture and Technology, Institute of Symbiotic Science and Technology, Professor, 大学院共生科学技術研究院, 教授 (50157187)
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| Co-Investigator(Kenkyū-buntansha) |
HASHIMOTO Hideya Meuji University, Faculty of Science and Technology, Professor, 理工学部, 教授 (60218419)
UDAGAWA Seiichi Nihon University, School of Medicine, Associate Professsor, 医学部, 助教授 (70193878)
TASAKI Hiroyuki University of Tsukuba, Graduate School of Pure and Applied Sciences, Associate Professor, 大学院数理物質科学研究科, 助教授 (30179684)
KODA Takashi Toyama University, Graduate School of Science and Engineering, Associate Professor, 大学院理工学研究部, 助教授 (40215273)
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| Project Period (FY) |
2004 – 2006
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| Keywords | Grassmann geometry / Spin(7) / Cayley calivration / submanifold / exterior product |
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| Research Abstract |
(1) We already classified the case that the image of Cartan embedding into compact simple Lie group are minimal and stable
if the Cartan embedding is defined by automorphism of order 2 or 3
if the Cartan embedding is defined by inner automorphisim of order 4
We classified the case that the image of Cartan embedding into compact if it is defined by outer automorphism of order 4.
(2) We classified 6-dimensional submanifolds of 8 dimensional Euclidean space which are invariant under the action of Spin(7) by joint work with Hashimoto, Koda and Sekigawa.
(3) We classified 3-dimensional submanifolds of 7-dimensional sphere with the property that the cone over the submanifold is calibrated by Cayley calibration.
(4) We considered a method of construction of invariant p-th exterior product of an irreducible representation of SU(2). And, as an example, we gave the invariant element in 3-rd exterior product of 11-dimesional SU(2)-irreducible representation.
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