A class of vertex operator algebras generated by Virasoro vectors

In this paper, we study a class of simple OZ-type vertex operator algebras $V$ generated by simple Virasoro vectors ${\omega }^{ij}={\omega }^{ji}$, $1\le i<j\le n$, $n\ge 3$. 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.