Jacobi trace functions in the theory of vertex operator algebras

Vertex operator algebras and the representation theory of toroidal algebras

An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras. AMS (MOS) Subject Classifications:17B69, 17B68, 17B66, 17B10.

On Clifford Theory of Vertex Operator Algebras

K-theory associated to vertex operator algebras

We introduce two K-theories, one for vector bundles whose fibers are modules of vertex operator algebras, another for vector bundles whose fibers are modules of associative algebras. We verify the cohomological properties of these K-theories, and construct a natural homomorphism from the VOA K-theory to the associative algebra K-theory.

(Pseudo-)Trace Functions and Modular Invariance of Vertex Operator Algebra

By including interlocked modules, we showed a modular invariance property of (pseudo) trace functions of modules for a 2-dimensional conformal field theory satisfying C 2-finiteness condition.

Vertex Operator Algebras And

Let V be a vertex operator algebra. We construct a sequence of associative algebras A n (V) (n = 0; 1; 2; :::) such that A n (V) is a quotient of A n+1 (V) and a pair of functors between the category of A n (V)-modules which are not A n?1 (V)-modules and the category of admissible V-modules. These functors exhibit a bijection between the simple modules in each category. We also show that V is r...