2021 Fiscal Year Final Research Report
On constructions of asid bimodules
| Project/Area Number |
18K13387
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | University of Yamanashi |
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Principal Investigator |
Yamaura Kota 山梨大学, 大学院総合研究部, 准教授 (60633245)
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| Project Period (FY) |
2018-04-01 – 2022-03-31
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| Keywords | asid加群 / 岩永-Gorenstein環 / 自明拡大環 / 導来圏 / 安定圏 |
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| Outline of Final Research Achievements |
From an algebra R and its bimodule C, one can construct a graded algebra so called the trivial extension. If the trivial extension is Iwanaga-Gorenstein, then the bimodule C is called an asid bimodule over R. In this study, we analyzed structures of asid bimodules, and obtained several results. For example, we had the following two observations of asid bimodules over some algebra R. Every asid bimodule is a direct sum of an asid bimodule whose asid number is one and a nilpotent bimodule with respect to tensor product. The set of all asid bimodules whose asid numbers are one have a structure of a group. In the context of these observations, we showed that the similar claims hold under suitable setting.
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| Free Research Field |
環の表現論
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| Academic Significance and Societal Importance of the Research Achievements |
本研究の対象であるasid加群は近年に導入・深く研究され，その表現論的意味が明らかになったばかりの加群である．従ってまだ，それほど知見が蓄積していない研究対象である．本研究により，asid加群の研究ではasid数1のasid加群およびその一般化が重要であり，そこには群という良い構造が現れること，適当な設定の下では傾複体との関係があることなどが示された．これにより，asid加群は既存の数学的対象と結びついており，豊かな構造を持つことがわかってきた．
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