Classification of simple weight modules for super-Virasoro algebra with a finite-dimensional weight space
- 时间:0
- 分类:O152.5[理学—数学;理学—基础数学] O177[理学—数学;理学—基础数学]
- 作者机构:[1]School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China
- 相关基金: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).
关键词:
VIRASORO代数, 有限维空间, 模块, 分类, 超弦理论, 无限维, 代数和, 权空间, Super-Virasoro algebra, Ramond algebra, weight module, Harish-Chandra module
中文摘要:
有有在超弦理论的特别重要性的 Virasoro 代数学的二延期:Ramond 代数学和 Neveu-Schwarz 代数学,它是 Virasoro 代数学的 2-graded 延期。在这份报纸,我们证明在有一个无限维的重量空格的 Ramond 代数学上的一个简单重量模块的支持与重量格子与一致并且重要重量空格和奇怪的部分或甚至模块的部分的所有交叉是无限维的。和我们在 Neveu-Schwarz 代数学上获得了的那的这结果为 Virasoro 代数学概括结果到 super-Virasoro 代数学。
英文摘要:
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.