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Generalized Vertex Algebras and Relative Vertex Operators Birkhauser Hardcover
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eBay-Artikelnr.:187187546281
Artikelmerkmale
- Artikelzustand
- Artist
- Not Specified
- PublishedOn
- 2012-12-21
- Title
- Generalized Vertex Algebras and Relative Vertex Operators
- ISBN
- 9781461267218
Über dieses Produkt
Product Identifiers
Publisher
Birkhäuser Boston
ISBN-10
1461267218
ISBN-13
9781461267218
eBay Product ID (ePID)
164638354
Product Key Features
Number of Pages
IX, 206 Pages
Language
English
Publication Name
Generalized Vertex Algebras and Relative Vertex Operators
Publication Year
2012
Subject
Algebra / Abstract, Functional Analysis, Algebra / General
Type
Textbook
Subject Area
Mathematics
Series
Progress in Mathematics Ser.
Format
Trade Paperback
Dimensions
Item Height
0.2 in
Item Weight
12.1 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Intended Audience
Scholarly & Professional
Reviews
"The presentation is smooth, self-contained and accessible with detailed proofs. The 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, "The presentation is smooth, self-contained and accessible with detailed proofs. The 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, "The presentation is smooth, self-contained and accessible with detailed proofs. The 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
Series Volume Number
112
Number of Volumes
1 vol.
Illustrated
Yes
Table Of Content
1 Introduction.- 2 The setting.- 3 Relative untwisted vertex operators.- 4 Quotient vertex operators.- 5 A Jacobi identity for relative untwisted vertex operators.- 6 Generalized vertex operator algebras and their modules.- 7 Duality for generalized vertex operator algebras.- 8 Monodromy representations of braid groups.- 9 Generalized vertex algebras and duality.- 10 Tensor products.- 11 Intertwining operators.- 12 Abelian intertwining algebras, third cohomology and duality.- 13 Affine Lie algebras and vertex operator algebras.- 14 Z-algebras and parafermion algebras.- List of frequently-used symbols, in order of appearance.
Synopsis
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 special but 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., 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 special but 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 rapidly-evolving theory of vertex operator algebras provides deep insight into many important algebraic structures. Vertex operator algebras can be viewed as "complex analogues" of both Lie algebras and associative algebras. The monograph is written in a n accessible and self-contained manner, with detailed proofs and with many examples interwoven through the axiomatic treatment as motivation and applications. It will be useful for research mathematicians and theoretical physicists working the such fields as representation theory and algebraic structure sand will provide the basis for a number of graduate courses and seminars on these and related topics., 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.
LC Classification Number
QA150-272
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