Study on infinite dimensional algebraic groups and Lie algebras, and application to quasi-periodic and aperiodic structures
Project/Area Number |
17K05158
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | University of Tsukuba |
Principal Investigator |
Morita Jun 筑波大学, 数理物質系(名誉教授), 名誉教授 (20166416)
|
Project Period (FY) |
2017-04-01 – 2023-03-31
|
Project Status |
Completed (Fiscal Year 2022)
|
Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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Keywords | 代数群 / リー代数 / 代数的K理論 / 局所アフィン・リー代数 / カッツ・ムーディ群 / スキーム / 四元数体 / 量子ビット / カッツ・ムーデイ群 / Kac-Moody 群 / 基本同値 / 群スキーム / 結晶構造 / 準周期構造 / 非周期構造 / 構造論 / 表現論 / アフィン・リー代数 / 単純群 / 乗法因子群 / 局所アフィン・ルート系 / 表現 |
Outline of Final Research Achievements |
(1)The structure of K_2SL_2(R) was determined for several prime numbers p_1,...,p_n, where R = [1/p_1,...,1/p_n]. (2) We classified minimal locally affine Lie algebras. This is a joint work with Yoji Yoshii. (3) We characterized affine Kac-Moody groups using schemes and Galois descert. This is a joint work with A. Pianzola and T. Shibata. (4) We discussed some infinite root system obtained from H4 root systems in quaternion division ring, and obtained a new application to quantum bits. This is a joint work with Robert Moody.
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Academic Significance and Societal Importance of the Research Achievements |
何れも有限次元および無限次元の代数群とリー代数に関わる基本的な研究成果である。新たな知見も多く含み、数学的な価値は高く、意義深いと認めとられる。
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Report
(7 results)
Research Products
(12 results)