Griess Algebras and Conformal Vectors in Vertex Operator Algebras Original Research Article

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.