Z-graded weak modules and regularity
arXiv:1104.2369 · doi:10.1007/s00220-012-1543-7
Abstract
It is proved that if any Z-graded weak module for vertex operator algebra V is completely reducible, then V is rational and C_2-cofinite. That is, V is regular. This gives a natural characterization of regular vertex operator algebras.
9 pages