| Project/Area Number |
26400209
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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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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Osaka Prefecture University |
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Principal Investigator |
Aizawa Naruhiko 大阪府立大学, 理学(系)研究科(研究院), 教授 (70264786)
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| Research Collaborator |
Isaac Phillip S.
Segar Jambulingam
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 共形対称性 / リー群・リー代数 / 超群・超代数とその拡張 / 表現論 / 微分方程式の対称性 / 次数付きリー群 / クリフォード代数 / 微分方程式 / 対称性 / リー群 / 拡張されたリー超群 / 国際研究者交流 / ブラジル：インド / リー代数の表現論 / 非エルミート演算子 / 国際研究者交流（インド, ブラジル） |
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| Outline of Final Research Achievements |
Spacetime symmetries are very fundamental notion in physics. If Einstein's relativity is not taken into account, the spacetime symmetries, which include scale transformation, are richer mathematical structure. The mathematical structure is nowadays called "conformal Galilei groups (CGG)". Despite their physical importance, they are not studied thoroughly yet. The purpose of the present project is to study CGG and their extensions, such as super or generalized super, extensively and apply the results to other fields of mathematics and theoretical physics.
Our main achievements are summarizes as follows: (i) introduction new extensions of CGG, (ii) classification of irreducible representations, (iii) derivation of differential equations whose symmetry is given by CGG. Especially, it is revealed that the wave equation of spin 1/2 particle has a extended CGA symmetry, (iv) a relation between generalized super CGG and the Clifford algebras is clarified.
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