Decomposition of the lattice vertex operator algebra V2Al

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

The Fixed Point Subalgebra of a Lattice Vertex Operator Algebra by an Automorphism of Order Three

We study the subalgebra of the lattice vertex operator algebra V√ 2A2 consisting of the fixed points of an automorphism which is induced from an order 3 isometry of the root lattice A2. We classify the simple modules for the subalgebra. The rationality and the C2-cofiniteness are also established.

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