| Project/Area Number |
11440052
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | University of Tsukuba |
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Principal Investigator |
MASUDA Tetsuya Univ. of Tsukuba, Institute of Math., Ass. Prof., 数学系, 助教授 (70202314)
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| Co-Investigator(Kenkyū-buntansha) |
TAIRA Kazuaki University of Tsukuba, Institute of Math., Prof., 数学系, 教授 (90016163)
KAJITANI Kunihiko University of Tsukuba, Institute of Math., Prof., 数学系, 教授 (00026262)
TAKEUCHI Mitsuhiro University of Tsukuba, Institute of Math., Prof., 数学系, 教授 (00015950)
KAKEHI Tomiyuki Univ. of Tsukuba, Institute of Math., Ass. Prof., 数学系, 助教授 (70231248)
MIYAMOTO Masahiko University of Tsukuba, Institute of Math., Prof., 数学系, 教授 (30125356)
伊藤 光弘 筑波大学, 数学系, 教授 (40015912)
木村 達雄 筑波大学, 数学系, 教授 (30022726)
森田 純 筑波大学, 数学系, 教授 (20166416)
佐々木 建昭 (佐々木 健昭) 筑波大学, 数学系, 教授 (80087436)
坂井 公 筑波大学, 数学系, 助教授 (20241797)
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| Project Period (FY) |
1999 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥14,400,000 (Direct Cost: ¥14,400,000)
Fiscal Year 2002: ¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2001: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2000: ¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 1999: ¥7,100,000 (Direct Cost: ¥7,100,000)
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| Keywords | quantum group / symmetric space / computer system / 差分方程式 / 熱核 / 4次元球面 / インスタントン / ユニタリー表現 / 数式処理 / 量子群の表現論 / 非可換微分幾何学 / ホモロジー代数学 / 数理物理学 / ファイバー束 / q-アナログ / ゲージ理論 / 代数幾何学 / 調和解析 / コニタリー表現論 / 非可換幾何学 / 量子多様体の非可換幾何 / 調和解析学 / 巡回(コ)ホモロジー / 量子ベクトル束の特性類 / 複素構造と表現論 / 数理物理学のモデル / グレプナー基底 / マルチクラスター計算機システム |
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| Research Abstract |
The target of this research had been put in such a high level so that we were not able to carry out all the projects on the occasion that we asked for this research grant. On the process of our research concerning the quantum symmetric space, we recognized a quantum 4-dimensional spheres which are not realized as the quantum symmetric space, and we also succeeded to have an explicit construction of a quantum vector bundle on such spaces which are regarded to be very basic in the direction of quantum gauge theories leaving lots of problems to be studied in the future. Then, at the same time, we faced to compute the cyclic cohomologies of those quantum manifolds so that we decided to use a special type of computer system which had never tried to use for such a problem coming from pure mathematics due to the extremely huge amount of computations by hands. However, this problem of computer aided computation is still left together with the tunung of the computer system itself. On the other hand, a general framework to deal with the objects which are so called the locally compact quantum groups was eventually finished and already submitted to a journal in France. By making use of this framework, we are now ready to proceed in the direction of the very detailed study of the explicitly given examples of the quantum groups of the non compact type.
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