2013 Fiscal Year Final Research Report
Torsion structures in triangulated categories
| Project/Area Number |
22540053
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 環論 / 圏論 |
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| Research Abstract |
We focused on torsion pairs in triangulated categories. Torsion pairs are basic framework in representation theory. They enable us to decompose a given triangulated category into subcategories. We aimed at studying mechanism of existing "good" torsion pairs and applying them. We have obtained the following results: (1) discovery of a "triangle of recollements" which induces high symmetry and a new triangle equivalence as an application. (2) introducing homotopy and derived categories of "n-complexes" and triangle equivalence of these categories to homotopy and derived categories of normal complexes over a suitable extension ring. (3) one to one correspondence of weak torsion pairs to torsion pairs in a quotient category.
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