Study on the structures and representations of infinite dimensional algebraic groups and Lie algebras, and applications to quasiperiodic structures

• Project/Area Number: 26400005
• Research Category: Grant-in-Aid for Scientific Research (C)
• 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, 教授 (20166416)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥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)
• 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

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,

Research Products

• [Int'l Joint Research] Saint Petersburg University(ロシア連邦)
• [Int'l Joint Research] Bar-Ilan University(Israel)
• [Int'l Joint Research] Xiamen University(China)
• [Int'l Joint Research] Bar-Ilan University(Israel)
• [Int'l Joint Research] Heinrich-Heine-Universitaet(Germany)
• [Journal Article] Locally loop algebras and locally affine Lie algebras (2015)
  • Author(s): Jun Morita, Yoji Yoshii
  • Journal Title: Journal of Algebra Volume: 440 Pages: 379-442
  • DOI: 10.1016/j.jalgebra.2015.05.018
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Word maps in Kac-Moody setting (2015)
  • Author(s): Elena Klimenko, Boris Kunyavskii, Jun Morita, Eugene Plotkin
  • Journal Title: Toyama Mathematical Journal Volume: 37 Pages: 25-54
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Simplicity of some twin tree automorphism groups with trivial commutation relations (2014)
  • Author(s): Jun Morita, Bertrand Remy
  • Journal Title: Canad. Math. Bull. Volume: 57 Pages: 390-400
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] Lac-Moody groups, simple groups and Schur multipliers (2017)
  • Author(s): Jun Morita
  • Organizer: Japan-Korea Workshop on Algebras and Combinatorics
  • Place of Presentation: Kusunoki Hall, Kumamoto University, Kumamoto City, Kumamoto Prefecture, Japan
  • Year and Date: 2017-02-09
  • Int'l Joint Research / Invited
• [Presentation] LTR to Kac-Moody groups (2016)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Tits systems, Kac-Moody groups and their applications (2016)
  • Author(s): Jun Morita
  • Organizer: The 7th International Conference on Representation Theory
  • Place of Presentation: Xiamen University, Xiamen, China
  • Year and Date: 2016-07-18
  • Int'l Joint Research / Invited
• [Presentation] Some topics on Kac-Moody groups (2016)
  • 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
  • Int'l Joint Research / Invited
• [Remarks] WELCOME TO MORITA'S HOME PAGE