Generalized Vertex Algebras and Relative Vertex Operators by Chongying Dong

Generalized Vertex Algebras and Relative Vertex Operators by Chongying Dong

In the past few years, vertex operator algebra theory has been growing both in intrinsic interest and in the scope of its interconnections with areas of mathematics and physics. The structure and representation theory of vertex operator algebras is deeply related to such subjects as monstrous moonshine, conformal field theory and braid group theory. Vertex operator algebras are the mathematical counterpart of chiral algebras in conformal field theory. In the Introduction which follows, we sketch some of the main themes in the historical development and mathematical and physical motivations of these ideas, and some of the current issues. Given a vertex operator algebra, it is important to consider not only its modules (representations) but also intertwining operators among the mod­ ules. Matrix coefficients of compositions of these operators, corresponding to certain kinds of correlation functions in conformal field theory, lead natu­ rally to braid group representations. In the specialbut important case when these braid group representations are one-dimensional, one can combine the modules and intertwining operators with the algebra to form a structure satisfying axioms fairly close to those for a vertex operator algebra. These are the structures which form the main theme of this monograph. Another treatment of similar structures has been given by Feingold, Frenkel and Ries (see the reference [FFR] in the Bibliography), and in fact the material de­ veloped in the present work has close connections with much work of other people, as we explain in the Introduction and throughout the text.

"The presentation is smooth, self-contained and accessible with detailed proofsThe introduction offers background and history about the generalized theory. It also uses examples to show some of the central techniques in VOA, thus offering pedagogical help to the readers. I think this book will benefit researchers in the field."

—Mathematical Reviews

SKU	Unavailable
ISBN 13	9780817637217
ISBN 10	0817637214
Title	Generalized Vertex Algebras and Relative Vertex Operators
Author	Chongying Dong
Series	Progress In Mathematics
Condition	Unavailable
Publisher	Birkhauser Boston Inc
Year published	1993-11-01
Number of pages	206
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.