| Project/Area Number |
26610009
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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 |
Algebra
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| Research Institution | Osaka Prefecture University |
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Principal Investigator |
Minamoto Hiroyuki 大阪府立大学, 理学(系)研究科(研究院), 准教授 (50527885)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | ホモロジー代数 / 導来圏 / 微分次数付圏 / 微分次数付フロベニウス代数 / A∞代数 / 微分次数付代数 / 導来普遍局所化 / 導来二重可換子環 / DG代数 / 圏論的代数幾何学 |
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| Outline of Final Research Achievements |
A ring R is a system of numbers which admits addition, subtraction and multiplication and that an R-module is a module which admits an action of R. Studying relationship between R-modules via homological algebra, requires enlarge rings into differential graded(DG) rings. In this project, I had studied basic theory of DG-rings. I found that a basic property of commutator rings does not hold for DG commutator rings. I introduced universal localization for DG-rings and applied it to classification problem of thick subcategories of the derived category of a ring.I computed Massey products on Yoneda algebra in terms of extensions of the modules and, as an application, gave a clear proof and generalization of Gugenheim-May Theorem. I showed that DG-Frobenius algebra possesses an A-infinity Nakayama automorphism.
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