Study of the structure of a tannakian category formed by equivalence classes of systems of linear inequalities over a number field
Project/Area Number |
20540030
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | Kanagawa Institute of Technology |
Principal Investigator |
FUJIMORI Masami Kanagawa Institute of Technology, 基礎・教養教育センター, 准教授 (20312093)
|
Project Period (FY) |
2008 – 2010
|
Project Status |
Completed (Fiscal Year 2010)
|
Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
|
Keywords | 代数学 / 数論 / ディオファントス近似 / 数体 / 線型不等式 / 淡中圏 / 代数群 / 表現 |
Research Abstract |
It is known that the equivalence classes of systems of linear inequalities which describe a rational approximation property of numbers are naturally identified with the representations of some group, but the whole body of the huge group is not clear yet. In this study, we have revealed via what algebraic group a classical system of linear inequalities which corresponds to the famous Roth inequality is considered a representation of the said huge group. We have also shown that arbitrary reductive groups appear in a natural manner as quotients of the above-mentioned huge group.
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Report
(5 results)
Research Products
(5 results)