* Introduces the fundamental theory of vertex operator algebras and its basic techniques and
examples.* Begins with a detailed presentation of the theoretical foundations and proceeds …

The goal of the present paper is to provide a mathematically rigorous foundation to certain
aspects of the theory of rational orbifold models in conformal field theory, in other words the …

Let $ V $ be a vertex operator algebra and $ g $ an automorphism of finite order. We
construct an associative algebra $ A_g (V) $ and a pair of functors between the category of …

Let $ V $ be a vertex operator algebra with a category $\mathcal {C} $ of (generalized)
modules that has vertex tensor category structure, and thus braided tensor category …

We demonstrate that, for vertex operator algebras of CFT type, $ C_2 $-cofiniteness and
rationality is equivalent to regularity. For $ C_2 $-cofinite vertex operator algebras, we show …

We classify all two-dimensional, unitary, rational conformal field theories with two primaries,
central charge c< 25, and arbitrary Wronskian index. In mathematical parlance, we classify …

We establish that the Lie algebra of weight 1 states in a (strongly) rational vertex operator
algebra is reductive, and that its Lie rank 1 is bounded above by the effective central charge …

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 …

We classify the self-dual (or holomorphic) vertex operator superalgebras of central charge
24, or in physics parlance the purely left-moving, fermionic 2-dimensional conformal field …

Let V be a simple vertex operator algebra and G a finite automorphism group of V such that
VG is regular. It is proved that every irreducible V G-module occurs in an irreducible g …