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Contact代数K(m,n)的不可约模的结构 被引量：1

The Structure of Irreducible Modules of the Contact Algebra K(m,n)
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摘要 利用广义限制李代数的概念和性质,研究Contact代数K(m,n)的不可约表示,给出了特征标高度大于等于2且小于p-3的不可约K(m,n)-模的结构. Let K = K（m,n） be a Contact algebra. By using the concept of generalized restricted Lie algebras, this paper deals with the irreducible representations of Contact algebra K（m, n） and determines the constructions of irreducible modules whose character height is bigger than or equal to 2 and less than p - 3.
作者 杨群广 蒋志洪
机构地区 同济大学数学系
出处 《数学年刊（A辑）》 CSCD 北大核心 2010年第2期229-238,共10页 Chinese Annals of Mathematics
基金 国家自然科学基金(No.10671142)资助的项目
关键词 Contact代数 广义限制李代数 特征标 不可约模 Contact algebra, Generalized restricted Lie algebras, Character height, Irreducible modules
分类号 O152.5 [理学—基础数学]
  • 相关文献

参考文献16

  • 1Shu Bin.The generalized restricted representations of graded Lie algebras of Caftan type[J].J Algebra,1997,194:157-177.
  • 2Strade H.Representations of the Witt algebra[J].J Algebra,1977,49:595-605.
  • 3Chang H.Uber Witt sche Lie-ringe[J].Abh Math Sere Uuiv Hamburg,1941,14:151-184.
  • 4Shen Guangyu.Graded modules for graded Lie algebras of Cartan type (I)[J].Sci Sinica,1986,29:570-581.
  • 5Shen Guangyu.Graded modules for graded Lie algebras of Cartan type (Ⅱ)[J].Sci Sinica,1986,29:1009-1019.
  • 6Shen Guangyu.Graded modules for graded Lie algebras of Cartan type (Ⅲ)[J].Chin Ann Math,1988,9B(4):404-417.
  • 7Hu Naihong.The graded modules for graded contact Caftan algebras[J].Comm Algebra,1994,22:4475-4497.
  • 8Hu Naihong.Irreducible constituents of graded modules for graded contact Lie algebras of Cartan type[J].Comm Algebra,1994,22:5951-5971.
  • 9Holmes R R.Simple modules with character height at most one for the restricted Witt algebras[J].J Algebra,2001,237:446-469.
  • 10Holmes R R,Zhang Chaowen.Some simple modules for the restricted Caftan-type Lie algebras[J].J Pure Appl Algebra,2002,173:135-165.

二级参考文献9

  • 1Shu B. The generalized restricted representations of graded Lie algebras of Cartan type[J]. J Algebra, 1997,194:157.
  • 2Strade H. Representations of the Witt algebra[J]. J Algebra, 1977,49:595.
  • 3Holmes R R. Simple modules with character height at most one for the restricted Witt algebras[J]. J Algebra, 2001,237 : 446.
  • 4Holmes R R. Zhang C. Some simple modules for the restricted Cartan-type Lie algebras [J]. J Pure Appl Algebra, 2002, 173 : 135.
  • 5Zhang C. On simple modules for the restricted Lie algebras of Cartan type[J]. Comm Algebra, 2002,30: 5393.
  • 6Zhang C. Representations of the restricted Lie algebras of Cartan type[J]. J Algebra, 2005,290: 408.
  • 7Shu B. The realizations of primitive p-envelopes and the support varieties for graded Cartan type Lie algebras[J]. Comm Algebra, 1997,25 : 3209.
  • 8Shu B. Generalized restricted Lie algebras and representations of the Zassenhaus algebra[J]. J Algebra, 1998,204: 549.
  • 9Strade H. Farnsteiner R. Modular Lie Algebras and their representations[M]. New York: Dekker, 1988.

共引文献3

同被引文献14

  • 1Strade H, Farnsteiner R. Modular Lie algebras and their representations [M]. New York: Dekker, 1988.
  • 2Shu B. The generalized restricted representations of graded Lie algebras of Cartan type [J]. J Algebra, 1997, 194:157-177.
  • 3Chang H. Uber Witt sche Lie-rlnge [J]. Abh Math Sem Univ Hamburg, 1941, 14:151-184.
  • 4Shen G Y. Graded modules for graded Lie algebras of cartan type (I) [J]. Sci Sinica, 1986, 29:570-581.
  • 5Shen G Y. Graded modules for graded Lie algebras of cartan type (II) [J]. Sci Sinica, 1986, 29:1009-1019.
  • 6Shen G Y. Graded modules for graded Lie algebras of cartan type (III) [J]. Chin Ann Math, 1988, 9B(4):404-417.
  • 7Hu N H. The graded modules for graded contact Cartan algebras [J]. Comm Algebra, 1994, 22:4475-4497.
  • 8Hu N H. Irreducible constituents of graded modules for graded contact Lie algebras of Cartan type [J]. Comm Algebra, 1994, 22:5951-5971.
  • 9Holmes R R. Simple modules with character height at most one for the restricted Witt algebras [J]. J Algebra, 2001, 237:446-469.
  • 10Holmes R R, Zhang C W. Some simple modules for the restricted Cartan-type Lie algebras [J]. J Pure Appl Algebra, 2002, 173:135 165.

引证文献1

数学年刊（A辑）
2010年 第2期

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