Certain Generating Subspaces for Vertex Operator Algebras

Minimal generating subspaces of “weak PBW type” for vertex operator algebras are studied and a procedure is developed for finding such subspaces. As applications, some results on generalized modules are obtained for vertex operator algebras that satisfy a certain condition, and a minimal generating space of weak PBW type is produced for VL with L any positive-definite even lattice.