Pure exactness of the principal cover of vertex operator algebras.

Let V be a vertex operator algebra. The fusion products in this paper are defined by logarithmic intertwining operators. Under this setting, we prove the pure exactness of any extension of the V -module V . Namely, if 0 → Q → ϵ P → ρ V → 0 is a short exact sequence of V -modules and W is a V -module, then 0 → Q ⊠ W → ϵ ⊠ 1 W P ⊠ W → ρ ⊠ 1 W V ⊠ W → 0 is also exact, where we view it as a sequence of g ( V ) -modules. [ABSTRACT FROM AUTHOR]