Key points are not available for this paper at this time.
We demonstrate that, for vertex operator algebras of CFT type, C 2 C₂ -cofiniteness and rationality is equivalent to regularity. For C 2 C₂ -cofinite vertex operator algebras, we show that irreducible weak modules are ordinary modules and C 2 C₂ -cofinite, V L + VL^+ is C 2 C₂ -cofinite, and the fusion rules are finite.
Abe et al. (Mon,) studied this question.