TKK代数的一类表示  

A Class of Representations of the TKK Algebra

作　　者：李鸿萍[1] 

机构地区：[1]厦门大学数学科学学院 福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2005年第4期453-457,共5页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(10371100)资助

摘　　要：研究对应于欧氏空间中最小半格S的Tits-Kantor-Koecher李代数G(T(S))的泛中心扩张G^(T(S))的表示,这里T(S)为关于半格S的Jordan代数.首先将该李代数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,构造了一组作用于Fock空间的顶点算子.最后通过验证所定义的顶点算子满足该无穷维李代数的所有幂级数等式,证明了这些顶点算子在这一Fock空间上给出了TKK李代数G^(T(S))的一个Boson场顶点表示.It was studied that the representation of the TKK algebraG(T(S)) which is the universal central extension of the Tits-Kantor-Koecher Lie algebraG(T(S)) obtained from the Jordan algebraT(S) with the smallest semilattice in the Euclidean space.The structure ofthe Lie algebra in terms of formal power series identities was expressed and the vertex operators acting on a Fock space from group algebra andsymmetric algebra was constructed.The construction is based on a result from the vertex construction of the glntype Lie algebra over the quan-tum torus. Finally,it was checked that the vertex operators satisfying all the power series indentities to see that the Fock space indeed givesa bosonic vertex representation of the TKK algebraG(T(S)).

关 键 词：K代数 Fock空间 顶点算子 Jordan 顶点表示 李代数 形式幂级数 对称代数 量子环面 中心扩张 欧氏空间 等式 无穷维 群代数 半格 

分 类 号：O153.1[理学—数学] TN201[理学—基础数学]