| Project/Area Number |
22740002
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | University of Tsukuba |
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Principal Investigator |
ABE Hiroki 筑波大学, 数理物質系, 研究員 (20533342)
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| Project Period (FY) |
2010 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
|
| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 環論 / 多元環の表現論 / 導来同値 / 傾斜鎖複体 / 傾斜加群 / 導来圏同値 / 準フロベニウス多元環 / ブラウアツリー |
|---|
| Research Abstract |
(1) We introduce the notation of reflections for selfinjective algebras and determine the transformations of Brauer trees associated with reflections. In particular, we provide a way to transform every Brauer tree into a Brauer line. (2) We show that every two-term tilting complex over an Artin algebra has a tilting module over a certain factor algebra as a homology group. Also, we determine the endomorphism algebra of such a homology group, which is given as a certain factor algebra of the endomorphism algebra of the two-term tilting complex. Thus, every derived equivalence between Artin algebras given by a two-term tilting complex induces a derived equivalence between the corresponding factor algebras.
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