Authors: Dražen Adamović, Victor G Kac, Pierluigi Möseneder Frajria, Paolo Papi, Ozren Perše
International Mathematics Research Notices, rny237,
Abstract: We discover a large class of simple affine vertex algebras , associated to basic Lie superalgebras at non-admissible collapsing levels , having exactly one irreducible -locally finite module in the category . In the case when is a Lie algebra, we prove a complete reducibility result for -modules at an arbitrary collapsing level. We also determine the generators of the maximal ideal in the universal affine vertex algebra at certain negative integer levels. Considering some conformal embeddings in the simple affine vertex algebras and , we surprisingly obtain the realization of non-simple affine vertex algebras of types and having exactly one nontrivial ideal.