A Characterization of Vertex Operator Algebra $${L(\frac{1}{2},0)\otimes L(\frac{1}{2},0)}$$

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

A vertex operator algebra structure of degenerate minimal models, I

We study fusion rings for degenerate minimal models (p = q) for N = 0, N = 1 and N = 2 (super)conformal algebras. In the first part we consider a family of modules for the Virasoro vertex operator algebra L(1, 0), and show that a fusion ring of the family is isomorphic to a Grothendieck ring Rep(sl(2,C)). In the second part, we used similar methods for the family of modules for N = 1 Neveu Schw...

A Characterization of the Moonshine Vertex Operator Algebra by Means of Virasoro Frames

In this article, we show that a framed vertex operator algebra V satisfying the conditions: (1) V is holomorphic (i.e, V is the only irreducible V -module); (2) V is of rank 24; and (3) V1 = 0; is isomorphic to the moonshine vertex operator algebra V \ constructed by Frenkel-Lepowsky-Meurman [12].