Simple restricted modules for Neveu-Schwarz algebra

2018/12/09 by Dong Liu, Liu, Dong, Yufeng Pei +3 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1812.03435

Abstract

In this paper, we give a construction of simple modules generalizing and including both highest weight and Whittaker modules for the Neveu-Schwarz algebra, in the spirit of the work of Mazorchuk and Zhao on simple Virasoro modules. We establish a 1-1 correspondence between simple restricted Neveu-Schwarz modules and simple modules of a family of finite dimensional solvable Lie superalgebras associated to the Neveu-Schwarz algebra. Moreover, for two of these superalgebras all simple modules are classified.

Cited by

• Simple smooth modules over the Lie algebras of polynomial vector fields
• Simple restricted modules of non-zero level over a deformed Heisenberg-Virasoro algebra

Related

• Classification of simple weight modules for the Neveu-Schwarz algebra with a finite-dimensional weight space
• Whittaker modules for the super-Virasoro algebras
• Simple smooth modules over the Ramond algebra and applications to vertex operator superalgebras
• On simple modules for the restricted Lie superalgebra gl(m|n)
• Simple Modules Over the Higher Rank Super-Virasoro Algebras