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一类TKK代数的Bosonic表示
  • 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（10931006）
作者： 夏章生[1]
关键词： TKK代数, Bosonic表示, 半格, TKK algebras, Bosonic representations, semilattices
中文摘要：

设S是Rn中＂最小＂的半格,在一个Jordan代数J（S）的基础上,通过所谓的Tits-Kantor-Koecher方法可构造TKK代数T（J（S））.首先给出了由任意一个量子环面Cq得到的李代数gl2（Cq）上的一个Bosonic表示,通过将TKK代数T（J（S））嵌入到一个特殊的量子环面对应的李代数gl2（Cq）中,得到了TKK代数T（J（S））的一个Bosonic表示.而且,也得到了这个TKK代数T（J（S））的表示的一个忠实的子表示.

英文摘要：

Let S be the ＂smallest＂ semilattice in Rn.From a Jordan algebra J（S）,using the so-called Tits-Kantor-Koecher construction,we can obtain TKK algebra T（J（S））.In this paper we first give a Bosonic representation of Lie algebra gl2（Cq） which is obtained from any a quantum torus Cq and prove that TKK algebra T（J（S）） can be embedded in the Lie algebra gl2（Cq） with respect to a special quantum torus.So we also give a Bosonic representation of TKK algebra T（J（S））.Besides,we also attain a faithful sub-representation of this representation for TKK algebra T（J（S））.

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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