Classification of vertex operator algebras of class ${\mathcal{S}}^4$ with minimal conformal weight one

Abstract

In this article, we describe the trace formulae of composition of several (up to four) adjoint actions of elements of the Lie algebra of a vertex operator algebra by using the Casimir elements. As an application, we give constraints on the central charge and the dimension of the Lie algebra for vertex operator algebras of class ${\mathcal{S}}^4$. In addition, we classify vertex operator algebras of class ${\mathcal{S}}^4$ with minimal conformal weight one under some assumptions.

17 pages

References in corpus (2)

• The intermediate vertex subalgebras of the lattice vertex operator algebras
• Norton's Trace Formulae for the Griess Algebra of a Vertex Operator Algebra with Larger Symmetry