华东师范大学学报(自然科学版) ›› 2008, Vol. 2008 ›› Issue (3): 51-58.

• 数学 统计学 • 上一篇    下一篇

广义Jacobson-Witt代数W(m;n)的I(x)约化表示(英)

李莎莎1, 舒斌2   

  1. 1. 山东理工大学 数学与信息科学学院, 山东淄博 255049; 2. 华东师范大学 数学系, 上海 200062
  • 收稿日期:2007-05-23 修回日期:2007-10-11 出版日期:2008-05-25 发布日期:2008-05-25
  • 通讯作者: 舒斌

I(x)-Reduced representations of generalized Jacobson-Witt algebras W(m;n)(English)

LI Sha-sha1, SHU Bin2   

  1. 1. School of Mathematics and Information Science, Shandong University of Technology, Zibo Shandong 255049, China 2. Department of Mathematics, East China Normal University, Shanghai 200062, China
  • Received:2007-05-23 Revised:2007-10-11 Online:2008-05-25 Published:2008-05-25
  • Contact: SHU Bin

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摘要： 推广了对限制李代数 W(m;1)的研究方法,研究了当特征p>2时的阶化Cartan型李代数W(m; n)的表示.特别地, 把对限制型李代数所用的降秩的方法推广到了非限制的情形. 描述了当x正则半单时W(m;n)的不可约广义x约化表示.

关键词: 阶化李代数, Cartan型, 正则半单, loop代数, 阶化李代数, Cartan型, 正则半单, loop代数

Abstract: This paper studied the representations of graded Cartan type Lie algebra W(m;n) in characteristic p>2, by generalizing the arguments of Shu's for restricted Lie algebras W(m;1). Especially, the rank-reducing method exploited in the restricted case was extended to non-restricted case. The simple
modules for W(m;n) with generalized p-character x were described by reduction when x was regular semisimple.

Key words: Cartan type, regular semisimple, loop algebra, graded lie algebra, Cartan type, regular semisimple, loop algebra

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