simple cartan-free modules of finite rank over the super-virasoro algebras

Abstract

We classify nontrivial simple super-Virasoro modules finitely generated over \(\C[L_0]\) using simple Laurent Weyl algebra modules finite free over \(\C[D]\). The classified modules are finite Cartan-free with equal parity ranks. We also prove finite length without simplicity and construct explicit nonsplit self-extensions.