A class of vertex operator algebras generated by Virasoro vectors

Runkang Feng

A class of vertex operator algebras generated by Virasoro vectors

Quantum Algebra 2025-10-13 v1

Authors: Runkang Feng

Abstract

In this paper, we study a class of simple OZ-type vertex operator algebras $V$ generated by simple Virasoro vectors $\omega^{ij}=\omega^{ji}$ , $1\leq i<j\leq n$ , $n\geq 3$ . We prove that $V$ is uniquely determined by its Griess algebra $V_2$ . The automorphism group of $V$ is also determined. Furthermore, we give the necessary conditions for $V$ to be unitary.

Keywords

vertex operator algebra Virasoro vector Griess algebra automorphism group unitarity OZ-type simple vertex operator algebra

Cite

@article{arxiv.2510.09397,
  title  = {A class of vertex operator algebras generated by Virasoro vectors},
  author = {Runkang Feng},
  journal= {arXiv preprint arXiv:2510.09397},
  year   = {2025}
}

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