On the structure of N-graded Vertex Operator Algebras

الأصل · EN

We consider the algebraic structure of N-graded vertex operator algebras with conformal grading V=⊕ₙ≥ ₀ Vₙ and V₀≥ 1. We prove several results along the lines that the vertex operators Y(a, z) for a in a Levi factor of the Leibniz algebra V₁ generate an affine Kac-Moody subVOA. If V arises as a shift of a self-dual VOA of CFT-type, we show that V₀ has a `de Rham structure' with many of the properties of the de Rham cohomology of a complex connected manifold equipped with Poincaré duality.