Decomposition of the Vertex Operator Algebra [formula]

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

1 7 D ec 1 99 9 Decomposition of the vertex operator algebra V √

A weight two vector v of a vertex operator algebra is called a conformal vector with central charge c if the component operators Lv(n) for n ∈ Z of Y (v, z) = ∑ n∈Z Lv(n)z −n−2 satisfy the Virasoro algebra relation with central charge c. In this case, the vertex operator subalgebra Vir(v) generated by v is isomorphic to a Virasoro vertex operator algebra with central charge c ([FZ], [M]). Let V...

Vertex Operator Algebra Structure of Standard Affine Lie Algebra Modules

On the Uniqueness of the Moonshine Vertex Operator Algebra

It is proved that the vertex operator algebra V is isomorphic to the moonshine VOA V ♮ of Frenkel-Lepowsky-Meurman if it satisfies conditions (a,b,c,d) or (a,b,c,d). These conditions are: (a) V is the only irreducible module for itself and V is C2-cofinite; (a) dimVn ≤ dimV ♮ n for n ≥ 3; (b) the central charge is 24; (c) V1 = 0; (d) V2 (under the first product on V ) is isomorphic to the Gries...