| Project/Area Number |
26400052
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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 | Osaka Prefecture University |
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Principal Investigator |
Kato Kiriko 大阪府立大学, 理学(系)研究科(研究院), 准教授 (00347478)
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| Research Collaborator |
Jorgensen P. Newcastle大学, 数学統計科, 教授
Christensen L. W. Texas工科大学, 数学統計科, 教授
NAKAOKA Hiroyuki 鹿児島大学, 理学部, 准教授
IIMA Kei-ichiro 国立奈良高専, 一般科, 准教授
ENOMOTO Haruhisa
NAKAMURA Tsutomu
MATSUI Hiroki
OGAWA Yasuaki
KUBO Yuki
HIRAYAMA Yukio
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 環論 / ホモロジー代数 / 圏論 |
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| Outline of Final Research Achievements |
If a triangulated category has a torsion pair, then it is a category of extensions of subcategories. Decomposition into subcategories makes analysis simpler. Sometimes existence of torsion pairs may characterize categories. Our results consist mainly of two points: (1) We studied generalized torsion pairs with milder condition on orthogonality. We showed that they correspond with torsion pairs of quotient categories. (2) We are interested in categories of N-complexes since it has N-gons of recollements which is multiplied and recursive recollements. As a consequence, we showed that a derived category of N-complexes over a ring is triangle equivalent to that of ordinary (2-)complexes of upper triangular matrix rings over the ring.
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