Hiroshi Yamauchi

<p>In this paper, we present a general construction of 3-transposition groups as automorphism groups of vertex operator algebras. Applying to the moonshine vertex operator algebra, we establish the Conway-Miyamoto correspondences between Fischer 3-transposition groups and and and Virasoro vectors of subalgebras of the moonshine vertex operator algebra.</p>

We study simple current extensions of tensor products of two vertex operator<br /> algebras satisfying certain conditions. We establish the relationship between<br /> the fusion rule for the simple current extension and the fusion rule for a<br /> tensor factor. In some special case, we construct a chain of simple current<br /> extensions. As an example, we obtain a chain of simple current extensions<br /> starting from the simple affine vertex operator algebra associated with<br /> $\widehat{sl}_2$ at level a positive integer $k$. The irreducible modules are<br /> classified and the fusion rules are determined for those simple current<br /> extensions.

We prove the uniqueness of the simple vertex operator algebra of OZ-type<br /> generated by Ising vectors of $\sigma$-type. We also prove that the simplicity<br /> can be omitted if the Griess algebra is isomorphic to the Matsuo algebra<br /> associated with the root system of type $A_n$.