LAUSR

Abstract In this paper, we construct a family of vertex operator algebras parameterized by a non-zero complex number r, whose Griess algebras V2 are isomorphic to Hermitian Jordan algebras of type C and A with . This extends the construction of Ashihara and Miyamoto for the type B case, therefore we can realize all Hermitian Jordan algebras as the Griess algebras of moonshine type vertex operator algebras. Our construction is analogous to the construction of the vertex operator algebra given by Kac and Radul. For all values of r we also prove the corresponding simplicity results of .