Memoirs of the American Mathematical Society 1993; 85 pp; softcover Volume: 106 ISBN10: 0821825712 ISBN13: 9780821825716 List Price: US$34 Individual Members: US$20.40 Institutional Members: US$27.20 Order Code: MEMO/106/507
 This book extends the Jacobi identity, the main axiom for a vertex operator algebra, to multioperator identities. Based on constructions of Dong and Lepowsky, relative \({\mathbf Z}_2\)twisted vertex operators are then introduced, and a Jacobi identity for these operators is established. Husu uses these ideas to interpret and recover the twisted Z operators and corresponding generating function identities developed by Lepowsky and Wilson for the construction of the standard \(A^{(1)}_1\)modules. The point of view of the Jacobi identity also shows the equivalence between these twisted Zoperator algebras and the (twisted) parafermion algebras constructed by Zamolodchikov and Fadeev. The LepowskyWilson generating function identities correspond to the identities involved in the construction of a basis for the space of Cdisorder fields of such parafermion algebras. Readership Mathematicians and physicists interested in vertex operators, Lie theory, conformal field theory, and string theory. Table of Contents  Introduction
 A multioperator extension of the Jacobi identity
 A relative twisted Jacobi identity
 Standard representations of the twisted affine Lie algebra \(A^{(1)}_1\)
 References
