Weyl groups and vertex operator algebras generated by Ising vectors satisfying the (2B, 3C) condition

Abstract

In this paper, we construct explicitly certain moonshine type vertex operator algebras generated by a set of Ising vectors I such that(1) for any e ≠ f ∈ I, the subVOA VOA (e, f) generated by e and f is isomorphic to either U2Bor U3C; and(2) the subgroup generated by the corresponding Miyamoto involutions {τe| e ∈ I} is isomorphic to the Weyl group of a root system of type An, Dn, E6, E7or E8.The structures of the corresponding vertex operator algebras and their Griess algebras are also studied. In particular, the central charge of these vertex operator algebras are determined.