2011 Fiscal Year Final Research Report
Two-term tilting complexes for selfinjective algebras
| 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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| Keywords | 環論 / 多元環の表現論 |
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| 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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