… and commutative diagrams of coherence theory for monoidal categories. This is not merely a
… the category of modules for a suitable vertex operator algebra is a vertex tensor category in …

… produces a braided tensor category in a natural way… vertex tensor category. Here we present
the fundamental properties of the P ( z )-tensor product of two modules for a vertex operator …

… algebra and on the products or iterates of two intertwining operators for the vertex operator
… when the vertex operator algebra is rational and products of two intertwining operators are …

… notion of tensor product of modules for a suitable vertex operator algebra, defined in … vertex
tensor category, and we announce that the category of modules for a rational vertex operator …

… Our theorem assumes only that the vertex operator algebra that we consider satisfies … the
braided tensor category structure on the category of modules for such a vertex operator algebra …

… Then we show that if a vertex operator algebra is selfcontragredient as a module for itself,
then the corresponding form is symmetric. Next we define intertwining operators and prove …

… on the torus for a given vertex operator algebra (Definition 4.1.1, … vertex operator algebra
gives rise to a system of correlation functions on the torus by taking q-trace of vertex operators …

… In Section 4, we study vertex operator algebras with different Virasoro elements and we also
construct a family of simple vertex operator algebras V with the properties that Vo is not one-…

… a braided fusion category. … category of ordinary modules of affine vertex operator superalgebra
L G ( 3 ) ( 1 , 0 ) . We prove that the category of ordinary modules of affine vertex operator …

… theory for modules for a suitable vertex operator algebra. In … constructs the much richer “vertex
tensor category” structure, which … 14, on the module category of a suitable vertex operator …