### 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 S^{4}. In addition, we classify vertex operator algebras of class S^{4} with minimal conformal weight one under some assumptions.

Original language | English |
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Pages (from-to) | 1369-1388 |

Number of pages | 20 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 68 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2016 Jan 1 |

### Keywords

- Deligne's exceptional Lie algebras
- Trace formula
- Vertex operator algebra

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Maruoka, H., Matsuo, A., & Shimakura, H. (2016). Classification of vertex operator algebras of class S

^{4}with minimal conformal weight one.*Journal of the Mathematical Society of Japan*,*68*(4), 1369-1388. https://doi.org/10.2969/jmsj/06841369