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

Abstract

In this paper, we show that $\sigma$-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 VOA are also discussed in details. In particular, we show that the automorphism group of the VOA $V_{K_{12}}^{\hat{\nu }}$ associated to the Coxeter Todd lattice $K_{12}$ contains a subgroup isomorphic to ${}^{+}{\Omega }^{-}(8,3)$.

arXiv comment38 pages