Simple smooth modules over the superconformal current algebra
Abstract
In this paper, we classify simple smooth modules over the superconformal current algebra $\mathfrak{g}$ with one mild condition on the center. More precisely, we first classify simple smooth modules over the Heisenberg-Clifford algebra, and then prove that any simple smooth $\mathfrak{g}$-module is a tensor product of a simple smooth module over the super Virasoro algebra and a simple smooth module over the Heisenberg-Clifford algebra, or an induced module from a simple module over some finite-dimensional solvable Lie superalgebras. As a byproduct, we provide characterizations for both simple highest weight $\mathfrak{g}$-modules and simple Whittaker $\mathfrak{g}$-modules. Additionally, we present some concrete simple smooth $\mathfrak{g}$-modules that are not tensor product of modules over the super Virasoro algebra and the Heisenberg-Clifford algebra.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Advanced Topics in Algebra
Nonlinear Waves and Solitons
Publication details
- Journal / source
- Pure and Applied Mathematics Quarterly
- Publisher
- International Press of Boston
- Volume
- 22
- Issue
- 3
- Pages
- 1003–1043
- Publication date
- 1 January 2026
- Language
- EN