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

摘要

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 U_(2B) or U_(3C); and (2) the subgroup generated by the corresponding Miyamoto involutions {τ_e | e ∈ I} is isomorphic to the Weyl group of a root system of type A_n, D_n, E_6, E_7 or E_8. 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.