| 广义TKK代数的一类Boson表示 |
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| 引用本文： | 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, 0(2): 235-240 |
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| 作者姓名： | 李鸿萍 |
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| 作者单位： | 华侨大学数学学院 |
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| 基金项目： | 华侨大学科研基金资助项目(10HZR24) |
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| 摘 要： | 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.
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| 关 键 词： | TKK代数 Boson场 Jordan代数 顶点算子表示 Fock空间 |
A Class of Boson Representations of the Extended TKK Algebra |
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| LI Hong-ping. A Class of Boson Representations of the Extended TKK Algebra[J]. Journal of Huaqiao University(Natural Science), 2012, 0(2): 235-240 |
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| Authors: | LI Hong-ping |
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| Affiliation: | LI Hong-ping(School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China) |
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| Abstract: | 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. |
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| Keywords: | TKK algebra Boson representations Jordan algebra vertex operator representation Fock space |
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