Study of Algebraic groups and Lie Algebras and Applications

代数群和李代数的研究及其应用

• 批准号: 11640008
• 负责人: MORITA Jun
• 金额: $ 2.05万
• 依托单位: University of Tsukuba
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640008/
• 关键词: Kac-Moody groups; Kac-Moody algebra; Gauss decomposition; カッツ・ムーディ群; ガウス分解; 単純群; 準結晶

The existence of strong Gauss decompositions for general Kac-Moody groups has been proved. In the case of finite dimensional semisimple algebraic groups such a result was given before by V. Chernousov etc. In the infinite dimensional case, several ,new properties as well,as strong Gauss decompositions have been established. More explicitely, we letG = a Kac-Moody group,Z(G) = the center of G,T = the standard maximal torus,U = the standard maximal upper triangular unipotent subgroup,V = the standard maximal lower triangular unipotent subgroup.Then the following has been shown to be-true for every h[0x81b8(Shift-JIS)]T :G=Z(G)[0x81be(Shift-JIS)][0x81be(Shift-JIS)]__<g[0x81b8(Shift-JIS)]G>g(VhU)g^<-1>.Furthermore, using this, it has been proved that every noncentral element is able to be expressed as a product of two unipotent elements, which is a very strong result to study the group structure of a Kac-Moody group. As related topics, positive cones and semigroups have been discussed, and Matsumoto type presentations have been given for certain K-seniigroups. Also, some quasi-periodic structures have been studied as applications of algebraic group theory and algebraic number theory.

已经证明了一般的Kac-Moody群体的强高斯分解存在。在有限的尺寸半密度代数组的情况下，Chernousov烟.等在无限尺寸的情况下给出了这样的结果。更明确地，我们让我们结识=一个kac-moody组，z（g）= g，t =标准的最大圆环，u =标准的标准最大最大上三角形单位子组，v = =标准的最大下三角单位单位子组。 :G=Z(G)[0x81be(Shift-JIS)][0x81be(Shift-JIS)]__<g[0x81b8(Shift-JIS)]G>g(VhU)g^<-1>.Furthermore, using this, it has been proved that every noncentral element is able to be expressed as a product of two unipotent elements, which is a very strong result to study the group structure of a Kac-Moody Group。由于已经讨论了相关主题，正面的锥和半群，并为某些K-谱系提供了松本类型的演示。此外，已经研究了一些准周期结构作为代数群体理论和代数数理论的应用。

项目成果

Tatsuya Kimijima, Jun Morita: "A certain algebraic construction of quasicrystals and their isomorphism classes"Journal of Physics A : Math.Gen. 33. 8483-8487 (2000)

Tatsuya Kimijima、Jun Morita：“准晶体及其同构类的某种代数构造”物理学杂志 A ：Math.Gen。

Robert Moody, Jun Morita: "Positivity for K_1 and K_2"Journal of Algebra. 229. 1-24 (2000)

罗伯特·穆迪 (Robert Moody)、森田淳 (Jun Morita)：“K_1 和 K_2 的正性”代数杂志。

Jun Morita, Eugene Plotkin: "Prescribed Gauss decompositions for Kac-Moody groups over fields"Rendiconfi del Seminario Matematico de lla Universifa di Padova. 106. 153-163 (2001)

Jun Morita，Eugene Plotkin：“域上 Kac-Moody 群的规定高斯分解”Rendiconfi del Seminario Matematico de lla Universifa di Padova。

Jun Morita, Kuniko Sakamoto: "Shell structure of dodecagonal quasicrystals associated with root system F_4 and cyclotomic field Q(ζ_<12> )"Communications in Algebra. 28. 256-263 (2000)

Jun Morita、Kuniko Sakamoto：“与根系 F_4 和分圆场 Q(ζ_<12> ) 相关的十二角准晶体的壳结构”通讯代数 28. 256-263 (2000)

Jun Morita, Engene Plotkin: "Prescribed Gauss decompositions for Kas-Moody groups over Fields"Rendiconti del Seminario Matenatice dela Universita di Padora. 106. 153-163 (2001)

Jun Morita，Engene Plotkin：“域上 Kas-Moody 群的规定高斯分解”Rendiconti del Seminario Matenatice dela Universita di Padora。