Extensions of the Jacobi identity for vertex operators and standard Aı⁽¹⁾-modules / Cristiano Husu.

Format:

Book

Author/Creator:

Husu, Cristiano, 1960- author.

Series:

Memoirs of the American Mathematical Society ; Number 507.

Memoirs of the American Mathematical Society, 0065-9266 ; Number 507

Language:

English

Subjects (All):

Vertex operator algebras.

Jacobi identity.

Modules (Algebra).

Representations of algebras.

Physical Description:

1 online resource (98 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1993.

Language Note:

English

Summary:

This book extends the Jacobi identity, the main axiom for a vertex operator algebra, to multi-operator identities. Based on constructions of Dong and Lepowsky, relative 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 Z-operator algebras and the (twisted) parafermion algebras constructed by Zamolodchikov and Fadeev. The Lepowsky-Wilson generating function identities correspond to the identities involved in the construction of a basis for the space of C-disorder fields of such parafermion algebras.

Contents:

""Table of Contents""; ""Introduction""; ""1 A multi�operator extension of the Jacobi identity""; ""2 A relative twisted Jacobi identity""; ""3 Standard representations of the twisted affine Lie algebra A[sup(1)][sub(1)]""; ""References""

Notes:

"November 1993, Volume 106, Number 507 (second of 6 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0084-7