Simple current extensions beyond semi-simplicity - Creutzig, Thomas; Kanade, Shashank; Linshaw, Andrew R. (Communications in Contemporary Mathematics, 2020)
Let V be a simple vertex operator algebra (VOA) and consider a representation category of V that is a vertex tensor category in the sense of Huang-Lepowsky. In particular, this category is a braided tensor category. Let J be an object in this category that is a simple current of order two of either integer or half-integer conformal dimension. We prove that V ⊕ J is either a VOA or a super VOA. If the representation category of V is in addition ribbon, then the categorical dimension of J decides this parity question. Combining with Carnahan's work, we extend this result to simple currents of arbitrary order. Our next result is a simple sufficient criterion for lifting indecomposable objects that only depends on conformal dimensions. Several examples of simple current extensions that are C2-cofinite and non-rational are then given and induced modules listed.
CRIS-Team Scopus Importer:2024-06-24
Keywords: simple current extensions; Vertex operator algebras