[1]李鸿萍.广义TKK代数的一类Boson表示[J].华侨大学学报(自然科学版),2012,33(2):235-240.[doi:10.11830/ISSN.1000-5013.2012.02.0235]
LI Hong-ping.A Class of Boson Representations of the Extended TKK Algebra[J].Journal of Huaqiao University(Natural Science),2012,33(2):235-240.[doi:10.11830/ISSN.1000-5013.2012.02.0235]
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广义TKK代数的一类Boson表示(
)
《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]
- 卷:
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第33卷
- 期数:
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2012年第2期
- 页码:
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235-240
- 栏目:
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- 出版日期:
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2012-03-20
文章信息/Info
- Title:
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A Class of Boson Representations of the Extended TKK Algebra
- 文章编号:
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1000-5013(2012)02-0235-06
- 作者:
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李鸿萍
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华侨大学数学学院
- Author(s):
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LI Hong-ping
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School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
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- 关键词:
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TKK代数; Boson场; Jordan代数; 顶点算子表示; Fock空间
- Keywords:
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TKK algebra; Boson representations; Jordan algebra; vertex operator representation; Fock space
- 分类号:
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O152.5
- DOI:
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10.11830/ISSN.1000-5013.2012.02.0235
- 文献标志码:
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A
- 摘要:
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研究对应于欧式空间中非格半格S的Tits-Kantor-Koecher(TKK)李代数g(T(S))的泛中心扩张广义TKK代数g(T(S))的一类Boson场表示.首先将广义TKK代数g(T)的结构等式表示为一系列形式幂级数等式,然后利用关于量子环面上gln型李代数的顶点表示及由群代数与对称代数组成的Fock空间,构造一组作用于Fock空间的顶点算子.最后,证明这些顶点算子在这Fock空间上给出了广义TKK代数g(T)的一个Boson场顶点表示.
- Abstract:
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In this paper,we study the representation of the extended Tits-Kantor-Koecher(TKK) algebra which is the universal central extension of the TKK Lie algebra obtained from the Jordan algebra which the non-lattice semi-lattice in the Euclidean space.The structure of the Lie algebra in terms of formal power series identities was constructed.The construction is based on a result from the vertex construction of the type Lie algebra over the quantum torus.Finally,it is proved that the vertex operators satisfying all the power series identities gives a Bosonic vertex representation of the Extended TKK algebra in the Fock space.
备注/Memo
- 备注/Memo:
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华侨大学科研基金资助项目(10HZR24)
更新日期/Last Update:
2014-03-23