  We incorporate a category of certain modules for an affine Lie algebra, of a
certain fixed non-positive-integral level, considered by Kazhdan and Lusztig,
into the representation theory of vertex operator algebras, by using the
logarithmic tensor product theory for generalized modules for a vertex operator
algebra developed by Huang, Lepowsky and the author. We do this by proving that
the conditions for applying this general logarithmic tensor product theory
hold. As a consequence, we prove that this category has a natural vertex tensor
category structure, and in particular we obtain a new, vertex-algebraic,
construction of the natural associativity isomorphisms and proof of their
properties.
