Study on the structures and representations of infinite dimensional algebraic groups and Lie algebras, and applications to quasiperiodic structures
| Project/Area Number |
26400005
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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 |
Algebra
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| Research Institution | University of Tsukuba |
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Principal Investigator |
MORITA Jun 筑波大学, 数理物質系, 教授 (20166416)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | algebraic group / Lie algebra / aperiodic structure / 代数群 / リー代数 / 準周期構造 / 単純群 / シュアー乗法因子群 / 分類問題 / 同型問題 / ルート系 / 建物理論 / 表現 / 非周期構造 |
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| Outline of Final Research Achievements |
The structures and representations of Kac-Noody groups as infinite dimensional algebraic groups are studied. In particular, the so-called simplicity problem is studied. In fact, the simplicity of some rank two Kac-Moody groups is established. On the other hand, the classification of locally extended affine Lie algebras is studied. Especially the classification problem, the maximality problem and the minimality problem are studied for locally affine Lie algebras. Furthermore, quasiperiodic and aperiodic structures are studied. And also associated algebraic structures are studied. In particular, using their representations, algorithms and programs are newly refined,
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Report
(4 results)
Research Products
(13 results)
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[Journal Article] Word maps in Kac-Moody setting2015
Author(s)
Elena Klimenko, Boris Kunyavskii, Jun Morita, Eugene Plotkin
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Journal Title
Toyama Mathematical Journal
Volume: 37
Pages: 25-54
Related Report
Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
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[Presentation] LTR to Kac-Moody groups2016
Author(s)
Jun Morita
Organizer
Summer Seminar on Lie Algebras
Place of Presentation
Kyoiku Gakubu 2nd Building, Iwate University, Morioka City, Iwate Prefecture, Japan
Year and Date
2016-08-26
Related Report
Int'l Joint Research / Invited
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[Presentation] Some topics on Kac-Moody groups2016
Author(s)
Jun Morita
Organizer
Infinite Dimensional Lie (Super)algebras and Their Representations
Place of Presentation
University of Isfahan, Isfahan, Iran
Year and Date
2016-05-25
Related Report
Int'l Joint Research / Invited
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