We give an example of an irrational C 2 -cofinite vertex operator algebra whose central charge is −2d for any positive integer d. This vertex operator algebra is given as the even part of the vertex operator superalgebra generated by d pairs of symplectic fermions, and it is just the realization of the c = −2-triplet algebra given by Kausch in the case d = 1. We also classify irreducible modules for this vertex operator algebra and determine its automorphism group.

Abstract. We demonstrate that, for vertex operator algebras of CFT type, C 2 -cofiniteness and rationality is equivalent to regularity. For C 2 -cofinite vertex operator algebras, we show that irreducible weak modules are ordinary modules and C 2 -cofinite, V + L is C 2 -cofinite, and the fusion rules are finite.

The fusion rules for the vertex operator algebras M (1) + (of any rank) and V + L

We completely determine fusion rules for irreducible modules of the charge conjugation orbifold V + L for a rank one even lattice L.