Abstract :
We define automorphisms of vertex operator algebra using the representations of the Virasoro algebra. In particular, we show that the existence of a special element, which we will call a “rational conformal vector with central charge image,” implies the existence of an automorphism of a vertex operator algebra. This result offers a simple construction of triality involutions of the Moonshine moduleVmusic natural. We also study the structures of Griess algebras and prove a conjecture given by Meyer Neutsch that the maximal dimension of associative subalgebras of the Griess Monster algebra is 48.
