The main axiom for a vertex operator algebra (over a field of characteris-
tic zero), the Jacobi identity, is extended to multi-operator identities. Then,
based on constructions of Dong and Lepowsky, relative Z2-twisted vertex op-
erators are introduced and a Jacobi identity for these operators is established.
These ideas are used to interpret and recover the twisted Z-operators and
corresponding generating function identities developed earlier by Lepowsky
and Wilson for the construction of the standard A{ -modules. The point of
view of the Jacobi identity also shows the equivalence between these twisted
Z-operator algebras and the (twisted) parafermion algebras constructed by
Zamolodchikov and Fateev. The Lepowsky-Wilson generating function iden-
tities correspond to the identities involved in the construction of a basis for
the space of C-disorder fields of such parafermion algebras.
This paper is a revised version of the author's thesis, written under the
direction of J. Lepowsky at Rutgers University.
Received by the editor August 12, 1991, and in revised form May 5, 1992.
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