A family of non-weight modules over the super-Virasoro algebras

• Published in: Journal of algebra Vol. 547; pp. 538 - 555
• Main Authors: Yang, Hengyun, Yao, Yufeng, Xia, Limeng
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.04.2020
• Subjects: Neveu-Schwarz algebra; Non-weight module; Ramond algebra; Simple module; 17B66; Ramond algebra; Non-weight module; 17B68; 17B10; 17B65; Simple module; Neveu-Schwarz algebra
• ISSN: 0021-8693; 1090-266X
• DOI: 10.1016/j.jalgebra.2019.11.025

In this paper, a family of non-weight modules over the super-Virasoro algebras are constructed. These modules over the Ramond algebra are free of rank 1 when restricted as modules over the Cartan subalgebra h, while these modules over the Neveu-Schwarz algebra are free of rank 2 when restricted as modules over the Cartan subalgebra H. We obtain a sufficient and necessary condition for such modules to be simple. Moreover, we determine the isomorphism classes of these modules. Finally, we show that these modules constitute a complete classification of free U(h)-modules of rank 1 over the super-Virasoro algebra of Ramond type, and also constitute a complete classification of free U(H)-modules of rank 2 over the super-Virasoro algebra of Neveu-Schwarz type.