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 S4. In addition, we classify vertex operator algebras of class S4 with minimal conformal weight one under some assumptions.
- Deligne's exceptional Lie algebras
- Trace formula
- Vertex operator algebra
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