Vertex operator algebras generated by Ising vectors of $$\sigma $$ σ -type

Abstract

We classify vertex operator algebras (VOAs) of OZ-type generated by Ising vectors of σ-type. As a consequence of the classification, we also prove that such VOAs are simple, rational, C 2 -cofinite and unitary, that is, they have compact real forms generated by Ising vectors of σ-type over the real numbers.