We show that if every module W for a vertex operator algebra V=∐ n∈ ℤV (n) satisfies the
condition dim W/C1 (W)<∞, where C1 (W) is the subspace of W spanned by elements of the …

Module categories of simple current extensions of vertex operator algebras - ScienceDirect
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We construct two non-semisimple braided ribbon tensor categories of modules for each
singlet vertex operator algebra M (p), p≥ 2. The first category consists of all finite-length M …

We describe the construction of the genus-zero parts of conformal field theories in the sense
of G. Segal from representations of vertex operator algebras satisfying certain conditions …

Vertex algebras are algebraic objects that encapsulate the concept of operator product
expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming …

0. Introduction. The category of finite direct sums of standard (integrable highest weight)
modules of a fixed positive integral level k for an affine Lie algebra ˆg is particularly …

This is the first part in a two-part series of papers constructing a unitary structure for the
modular tensor category (MTC) associated to a unitary rational vertex operator algebra …

Vertex operator algebra theory is a new area of mathematics. It has been an exciting and
ever-growing subject from the beginning, starting even before R. Borcherds introduced the …

Much of algebra and representation theory can be formulated in the general framework of
tensor categories. The aim of this paper is to further develop this theory for braided tensor …

The main result is that the category of ordinary modules of an affine vertex operator algebra
of a simply laced Lie algebra at admissible level is rigid and thus a braided fusion category …