On 3-transposition groups generated by σ-involutions associated to c=4/5 Virasoro vectors

In this paper, we show that σ-involutions associated to extendable c=4/5 Virasoro vectors generate a 3-transposition group in the automorphism group of a vertex operator algebra (VOA). Several explicit examples related to lattice VOAs are also discussed in detail. In particular, we show that the automorphism group of the VOA VK12νˆ associated to the Coxeter-Todd lattice K12 contains a subgroup isomorphic to Ω−+(8,3).