| Project/Area Number |
25800022
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Kagoshima University |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2014: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 三角圏 / 完全圏 / biset関手 / Mackey関手 / Burnside環 / 丹原関手 / derivator / ねじれ対 / ルコルマン / biset functor / Mackey functor / 2-category / triangulated category / torsion pair / ホモロジー代数 / アーベル圏 |
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| Outline of Final Research Achievements |
(1)Twin cotorsion pair on a triangulated category gives a simultaneous generalization of t-structure, cluster tilting subcategory and functorially finite rigid subcategory. We have given a condition for the heart of twin cotorsion pairs to be equivalent, by means of the associated functors.
(2)We have calculated the prime spectrum of the Burnside Tambara functor for a special kind of groups, and related it to the spectrum of the Burnside ring itself. We have also given a biset deformation of Tambara functors, which was known to Mackey functors.
We have shown that biset functors can be realized as a special kind of Mackey functors on a 2-category. Based on this result, describing the properties of multiplicative transfers of Burnside rings, we have revealed their 'partial Tambara' property。Besides, via the 2-category of finite groupoids, we have given a method to obtain a biset functor from a derivator on this 2-category.
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