Representations of the Nappi–Witten vertex operator algebra

Representations of vertex operator algebras

This paper is an exposition of the representation theory of vertex operator algebras in terms of associative algebras An(V ) and their bimodules. A new result on the rationality is given. That is, a simple vertex operator algebra V is rational if and only if its Zhu algebra A(V ) is a semisimple associative algebra. 2000MSC:17B69

The radical of a vertex operator algebra

Each v ∈ V has a vertex operator Y (v, z) = ∑ n∈Z vnz −n−1 attached to it, where vn ∈ EndV. For the conformal vector ω we write Y (ω, z) = ∑ n∈Z L(n)z . If v is homogeneous of weight k, that is v ∈ Vk, then one knows that vn : Vm → Vm+k−n−1 and in particular the zero mode o(v) = vwtv−1 induces a linear operator on each Vm. We extend the “o” notation linearly to V, so that in general o(v) is the...

A Characetrization of Vertex Operator Algebra L(

It is shown that any simple, rational and C2-cofinite vertex operator algebra whose weight 1 subspace is zero, the dimension of weight 2 subspace is greater than or equal to 2 and with central charge c = 1, is isomorphic to L(12 , 0) ⊗ L( 1 2 , 0). 2000MSC:17B69

Vertex Operator Algebra Structure of Standard Affine Lie Algebra Modules

Representations of Ternary Code Vertex Operator Algebras