Constructing structure theories of quandles and discrete symmetric spaces
| Project/Area Number |
16K13757
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Osaka City University (2018)
Hiroshima University (2016-2017) |
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Principal Investigator |
Tamaru Hiroshi 大阪市立大学, 大学院理学研究科, 教授 (50306982)
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | カンドル / 対称空間 / 幾何学 |
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| Outline of Final Research Achievements |
We obtained results on disconnected flat quandles and on symmetry-commutative subsets in quandles. In the former, we construct disconnected flat quandles from any graph, and proved that the constructed quandle is homogeneous if and only if the graph is vertex-transitive. In the latter, we defined the notion of symmetry-commutative subsets in quandles, and determined them for many cases, such as oriented Grassmannians and compact classical Lie groups.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究では，対称空間論を参考として，様々な概念や手法をカンドルに対して導入し，その性質を明らかにしている。対称空間論とカンドルを結びつける研究は独自のものであり，新たな研究領域を開拓しているものだと考える。さらにカンドルの研究を通して，対称空間の研究にも新たな知見が付け加えられている。
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Report
(4 results)
Research Products
(31 results)
