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多重Loop李代数的Weyl模
  • ISSN号：0438-0479
  • 期刊名称：《厦门大学学报：自然科学版》
  • 时间：0
  • 分类：O152.5[理学—数学;理学—基础数学]
  • 作者机构：[1]厦门大学数学科学学院,福建厦门361005
  • 相关基金：国家自然科学基金资助项目（10931006）
作者： 常学武[1]
关键词： 多重Loop代数, WEYL模, 诱导模, iterated Loop algebra, Weyl module, induced module
中文摘要：

设g为任意有限维复单李代数及Aν=C[t1±1,…,tν±]为ν个交换变量的Laurent多项式环.令L（g）=g C[t1±1,…,tν±]为多重Loop李代数.考虑L（g）上的Weyl模,证明了这类模都是有限维的,并且在适当的条件下证明了由一个元素生成的多重Loop代数的模一定是Weyl模的同态像.最后给出了Weyl模的一个张量积分解.

英文摘要：

Let g be any finite-dimensional simple Lie algebra over the complex field C and Aν=C[t±11,…,t±1ν] be the Laurent polynomial ring in ν commutating variables.Let L（g）=g C[t±11,…,t±1ν] be an iterated loop algebra.We consider the Weyl modules over L（g）.We prove that the Weyl modules are finite-dimensional and any module under some assumption is a quotient of such a module.Finally,we give a tensor product decomposition for the Weyl modules.

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期刊信息
  • 《厦门大学学报：自然科学版》
  • 中国科技核心期刊
  • 主管单位:中华人民共和国教育部
  • 主办单位:厦门大学
  • 主编：谢素原
  • 地址：厦门市思明南路422号厦门大学嘉庚三 817-819室
  • 邮编：361005
  • 邮箱：jxmu@xmu.edu.cn
  • 电话：0592-2180367 2187731
  • 国际标准刊号：ISSN：0438-0479
  • 国内统一刊号：ISSN：35-1070/N
  • 邮发代号:34-8
  • 获奖情况:
  • 多次被评为全国、华东地区、福建省的优秀科技期刊,2001年入选国家新闻出版总署评定的"中国期刊方阵",2003年获国家新闻出版总署颁发的"第二届国家科技...,2006年获国家教育部科技司颁发的"首届中国高校精...
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  • 被引量:16575