tame noncommutative projective schemes and related representation
| Project/Area Number |
18K03220
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Osaka Prefecture University |
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Principal Investigator |
Minamoto Hiroyuki 大阪府立大学, 理学(系)研究科(研究院), 准教授 (50527885)
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| Project Period (FY) |
2018-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 前射影的代数 / 箙Heisenberg代数 / 非可換射影スキーム / tame多様体 / 根基冪近似 / 局所自由層 / quiver Heisenberg / AR triangles / cluster roots / 非可換代数幾何学 / Calabi-Yau代数 / 導来圏 |
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| Outline of Final Research Achievements |
Originally I planed to investigate general theory of tame noncommutative projective scheme (=noncommutative projective schemes of graded Noetherian algebras). However, at the beginning stage, I found a class of algebras, so called Quiver Heisenberg algebras (QHA), in the collaboration with M. Herschend. Since it was expected to provide a nice and important class of graded Noetherian algebras, I have mainly studied QHA throughout this period. I introduced deformation parameter to QHA and by making use of this parameter, I was able to establish many result among other things universal Auslander-Reiten triangle and approximation by powers of the radical functors theorem over a field of arbitrary characteristic . In particular these result can be looked as a categorification of dimension formula of QHA of Dynkin quivers by Etingf-Rains.
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| Academic Significance and Societal Importance of the Research Achievements |
箙Qから構成される前射影的代数は箙の表現論から産み出された。Lie理論、代数幾何、数理物理にも現れる重要な数学的対象である。今回の研究では箙Heisenberg代数も道代数の表現論から産み出され、そして前射影的代数の一次元高い類似的性質を持つことを明らかにした。前射影的代数と同様に箙Heisenberg代数も重要な数学的対象であることが期待できる。
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Report
(5 results)
Research Products
(15 results)
