Mathematical analysis

Vertex operator algebra

Lie conformal algebra

Lie superalgebra

Affine transformation

Combinatorics

Physics

Graph

Pure mathematics

Mathematics

Cellular algebra

Virasoro algebra

Quantum mechanics

Degenerate energy levels

Algebra over a field

Superalgebra

Symmetric tensor

Exact solutions in general relativity

Affine Lie algebra

Vertex (graph theory)

Tensor (intrinsic definition)

Current algebra

Jordan algebra

Algebra representation

Communications in Contemporary Mathematics

We show that direct limit completions of vertex tensor categories inherit vertex and braided tensor category structures, under conditions that hold for example for all known Virasoro and affine Lie algebra tensor categories. A consequence is that the theory of vertex operator (super)algebra extensions also applies to infinite-order extensions. As an application, we relate rigid and non-degenerate vertex tensor categories of certain modules for both the affine vertex superalgebra of $\mathfrak{osp}(1|2)$ and the $N=1$ super Virasoro algebra to categories of Virasoro algebra modules via certain cosets.

Direct limit completions of vertex tensor categories