Simple current extensions beyond semi-simplicity

By T. Creutzig, Shashank Kanade, A. Linshaw. Communications in Contemporary Mathematics, 2015

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Let [Formula: see text] be a simple vertex operator algebra (VOA) and consider a representation category of [Formula: see text] that is a vertex tensor category in the sense of Huang–Lepowsky. In particular, this category is a braided tensor category. Let [Formula: see text] 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 [Formula: see text] is either a VOA or a super VOA. If the representation category of [Formula: see text] is in addition ribbon, then the categorical dimension of [Formula: see text] 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 [Formula: see text]-cofinite and non-rational are then given and induced modules listed.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9190dff54a54d2d1b75b4b52c6b421fae5892162

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Citations in the corpus

Braided Tensor Categories of Admissible Modules for Affine Lie Algebras (2017, methodology): “rtex operator algebra extensions [HKL, CKM] to construct a corresponding category of aﬃne vertex operator algebra modules as the category of local modules of an inﬁnite order simple current extension [CKL]. 1.2 Conjectures and the case of g= sl2 In the case of ℓ + h∨ ∈ Q ≥0 or ℓ ∈ Z +, the most diﬃc”