一类扭的Heisenberg-Virasoro顶点代数到βγ-系统的嵌入  

An Embedding of the Twisted Heisenberg-Virasoro Vertex Algebra into the βγ-system

作　　者：程俊芳[1] 楚彦军[1,2] 

机构地区：[1]河南大学数学与统计学院,河南开封475004 [2]河南大学现代数学研究所,河南开封475004

出　　处：《河南大学学报（自然科学版）》2017年第3期367-371,共5页Journal of Henan University:Natural Science

基　　金：国家自然科学基金数学天元青年基金资助项目(11526075);河南省高等学校重点科研项目(17A110003);河南大学基本科研业务费科研专项--青年科研人才种子基金资助项目(ZZJJ20140025)

摘　　要：扭的Heisenberg-Virasoro代数是圆周上的阶数小于等于1的微分算子李代数的万有中心扩张.它含有Heisenberg代数和Virasoro代数两个子代数.作为数学物理中的一类重要的李代数,它们具有Heisenberg顶点算子代数和Virasoro顶点算子代数的双重结构.因此,对这类顶点算子代数结构的研究在数学物理中有重要的理论意义.本文通过共形场论中顶点算子的算子积展开的方法把扭的Heisenberg-Virasoro代数由βγ-自由场实现,并把它们实现为βγ-系统中的一个共形顶点算子子代数.这种共形嵌入关系有助于理解由扭的Heisenberg-Virasoro顶点算子代数所提供的共形场理论的对称结构.The twisted Heisenberg-Virasoro algebra is the universal central extension of the Lie algebra of differential operators on a circle of order at most one. It contains the classical Heisenberg algebra and the Virasoro algebra as subalgebras. For such an important class of Lie algebras in mathematical physics, they inherit double structures of Heisenberg vertex operator algebra and Virasoro vertex operator algebra. Hence it is theoretically important to study this class of vertex operator algebras in mathematical physics. In this paper, we used operator product expansions of vertex operators to realize the twisted Heisenberg-Virasoro algebra as a conformal vertex operator subalgebra of βγ- system by βγ-free fields. This conformal embedding relation can help us to understand symmetries which are provided by the twisted Heisenberg-Virasoro vertex operator algebra in conformal field theory.

关 键 词：顶点代数 扭的Heisenberg—Virasoro代数 βγ-系统 

分 类 号：O152.5[理学—数学]