2012 Fiscal Year Final Research Report
Equivalences of derived categories of algebras and Lie algebras realized by Ringel-Hall algebras of algebras
| Project/Area Number |
21540036
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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 | Shizuoka University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
YAMAGATA Kunio 東京農工大学, 工学研究院, 教授 (60015849)
MORI Izuru 静岡大学, 理学部, 准教授 (50436903)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 多元環 / 導来圏 / グロタンディーク構成 / 被覆 / ラックス関手 / ホール代数 |
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| Research Abstract |
Let k be a commutative ring, I a small category and denote by k-Cat the 2-category of small k-categories. For 2-categories B, C, denote by Colax(B,C) the 2-category consisting of the colax functors from B to C and the lax transformations between them. We proved that each pseudofuncor C→D of 2-categories induces a pseudofunctor Colax(B,C)→Colax(B,D) for all 2-categories B, and defined the "module category", the "derived category", and derived equivalences of colax functors I→k-Cat by using it. We proved that if two such colax functors are derived equivalent, then so are their Grothendieck constructions, by which we gave a way to glue derived equivalences together.
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[Presentation] Quantum Beilinson algebras2010
Author(s)
Izuru Mori
Organizer
Test problems for the theory of finite dimensional algebras
Place of Presentation
Banff International Research Station, Banff, Canada
Year and Date
2010-09-16
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