| Project/Area Number |
15K04818
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kyoto University of Education |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 高次元配列 / テンソル / 群作用 / 不変式 / サグビー基底 / 日比環 / グレブナー基底 |
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| Outline of Final Research Achievements |
High dimensional array of data are called tensors in the field of data analysis. We considered in this research group actions to tensors with entries in a commutative ring.
We found that in many situations, there are rings of invariants whose initial algebra is the Ehrhart ring of a convex polytope. In particular, there are many cases that such Ehrhart rings are Hibi rings. Thus, we studied Hibi rings and obtained several results. Further, we defined a notion Doset Hibi ring and showed that the initial algebra of a certain rings of invariants have structures of Doset Hibi rings.
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