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)(R)(+),which is a VOA over the real number field R and has a positive definite invariant bilinear form, and such that its complexification CW(0)(R)(+) is a direct sum of the 3-state Potts model L(4/5, 0) and its module L(4/5, 3). As an application, we define an automorphism of order 3 of a VOA V-R over R if V-R contains W(0)(R)(+) as a sub VOA. (C) 2001 Academic Press.