顶点算子代数表示理论中的范畴和函子  

Categories and functors in the representation theory of vertex operator algebras

作　　者：姜翠波 林宗柱 

机构地区：[1]上海交通大学数学科学学院,上海200240 [2]Department of Mathematics,Kansas State University

出　　处：《中国科学：数学》2017年第11期1579-1594,共16页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11371245和11531004)资助项目

摘　　要：本文的主要目的是,用范畴的语言对顶点算子代数理论中的一些构造加以解释,同时将Abel范畴工具应用到顶点算子代数的研究中.本文将顶点算子代数范畴中的共形同态放宽为半共形同态,同时讨论半共形同态所对应的模范畴之间的函子性质.这样陪集构造可以实现为Hom函子,并利用Hom函子讨论相关性质.作为一个应用,本文构造了Jacquet函子,并讨论了它的性质.In this paper, we use the language of categories to describe representation theory of vertex operator algebras. The category of all vertex operator algebras and the category of modules of a vertex operator algebra are discussed. A homomorphism between two vertex operator algebras should preserve the Virasoro vectors, which is equivalent to commuting with the operators L（n） for all n ∈ Z. We expand the morphisms of this category so that morphisms are semi-conformal in the sense that they commute with those L（n） with n ≥ 0. This expansion does not change the classification of problem and makes the category into a tensor category. The coset construction becomes more natural in this category and relations between the module categories of vertex operator algebras can be described in terms of Hom-functors. As an application, we also construct the corresponding Jacquet functors. The semi-conformal vertex operator subalgebras plays the role of the Levi subgroups of a reductive group.

关 键 词：顶点算子代数 半共形同态 Jacquet函子 

分 类 号：O152.5[理学—数学]