Logarithmic intertwining operators and associative algebras

Abstract

We establish an isomorphism between the space of logarithmic intertwining operators among suitable generalized modules for a vertex operator algebra and the space of homomorphisms between suitable modules for a generalization of Zhu's algebra given by Dong-Li-Mason.

arXiv comment41 pages. The statement of Lemma 5.5 in the published version is wrong because it is not compatible with the definitions of $A_N(W)$ and the right action of $V$ on $W$ in the original version. These definitions are modified. The proofs of Lemma 4.4, Lemma 4.6, Theorem 4.7 are also modified accordingly. Lemma 5.5 is correct with the modified definitions