There are two extensions of Virasoro algebra with particular importance in superstring theory： the Ramond algebra and the Neveu-Schwarz algebra, which are Z2-graded extensions of the Virasoro algebra. In this paper, ...There are two extensions of Virasoro algebra with particular importance in superstring theory： the Ramond algebra and the Neveu-Schwarz algebra, which are Z2-graded extensions of the Virasoro algebra. In this paper, we show that the support of a simple weight module over the Ramond algebra with an infinite-dimensional weight space coincides with the weight lattice and that all intersections of non-trivial weight spaces and odd part or even part of the module are infinite-dimensional. This result together with the one that we have obtained over the Neveu-Schwarz algebra generalizes the result for the Virasoro algebra to the super-Virasoro algebras.展开更多
基金The research presented in this paper was carried out during the visit of author to Wilfrid Laurier University, Canada. The author thanks Wilfrid Laurier University for hospitality. The author would like to thank Prof. K. Zhao for stimulating discussion. The author also thanks the referees for good suggestions. This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11271165, 11471333） and the Natural Science Foundation for Colleges and Universities in Jiangsu Province （No. 14KJBll0006）.
文摘There are two extensions of Virasoro algebra with particular importance in superstring theory： the Ramond algebra and the Neveu-Schwarz algebra, which are Z2-graded extensions of the Virasoro algebra. In this paper, we show that the support of a simple weight module over the Ramond algebra with an infinite-dimensional weight space coincides with the weight lattice and that all intersections of non-trivial weight spaces and odd part or even part of the module are infinite-dimensional. This result together with the one that we have obtained over the Neveu-Schwarz algebra generalizes the result for the Virasoro algebra to the super-Virasoro algebras.
