3-State Potts Model and Automorphisms of Vertex Operator Algebras of Order 3

We study the fusion rules of a vertex operator algebra W(0)+ , which is a VOA over the real number field and has a positive definite invariant bilinear form, and such that its complexification W(0)+ is a direct sum of the 3-state Potts model L( , 0) and its module L( , 3). As an application, we define an automorphism of order 3 of a VOA V over if V contains W(0)+ as a sub VOA.