Generalized Vertex Algebras and Relative Vertex Operators by Chongying Dong

Cover of: Generalized Vertex Algebras and Relative Vertex Operators | Chongying Dong

Published by Birkhäuser Boston, Imprint: Birkhäuser in Boston, MA .

Written in English

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Subjects:

  • Group theory,
  • Mathematics,
  • Operator theory,
  • Topological groups,
  • Algebra

Edition Notes

Book details

Statementby Chongying Dong, James Lepowsky
SeriesProgress in Mathematics -- 112, Progress in Mathematics -- 112
ContributionsLepowsky, J. (James)
Classifications
LC ClassificationsQA150-272
The Physical Object
Format[electronic resource] /
Pagination1 online resource (ix, 206 p.)
Number of Pages206
ID Numbers
Open LibraryOL27040818M
ISBN 101461267218, 1461203538
ISBN 109781461267218, 9781461203537
OCLC/WorldCa853258386

Download Generalized Vertex Algebras and Relative Vertex Operators

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 : Paperback.

Vertex operator algebras can be viewed as "complex analogues" of both Lie algebras and associative algebras. They are mathematically precise counterparts of what are known in physics as chiral algebras, and in particular, they are intimately related to string theory and conformal field theory.

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.- PDF | On Jan 1,Chongying Dong and others published Generalized Vertex Algebras and Relative Vertex Operators | Find, read and cite all the research you need on ResearchGate.

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.

Generalized Vertex Algebras and Relative Vertex Operators 作者: Dong, Chongying/ Lepowsky, James 出版社: Springer Verlag 出版年: 页数: 定价: $ 装帧:. Vertex operators appeared in the early days of string theory as local operators describing propagation of string states.

Mathematical analogues of these operators were discovered in representation theory of affine Kac-Moody algebras in the works of Lepowsky–Wilson [LW] and I. Frenkel–Kac [FK]. Abstract. Now we return to the setting of Chapter 5. The axioms for a generalized vertex operator algebra do not quite apply to the structure of Ω *, the vacuum space () (for the Heisenberg algebra (ĥ *) z) equipped with the relative vertex operators Y *.In fact, the finite-dimensionality axiom () and the boundedness axiom () fail to hold in general, since L is not necessarily Author: Chongying Dong, James Lepowsky.

Contents 1 Introduction 1 2 The setting 15 3 Relative untwisted vertex operators 19 4 Quotient vertex operators 27 5 A Jacobi identity for relative untwisted vertex.

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 --   It is proved that for any vector space W, any set of parafermion-like vertex operators on W in a certain canonical way generates a generalized vertex algebra in the sense of Dong and Lepowsky with W as a natural module.

As an application, generalized vertex algebras are constructed from the Lepowsky–Wilson Z-algebras of any nonzero by: to Riemann surfaces of genus 0).

The generalized equalities then obtained are called the McKay-Thompson series. The space V = M n=0 V n constitutes an infinite-dimensional graded module of M.

Acted on by the Monster, it admits in fact a structure of vertex algebra, known as the Monster vertex algebra. The latter notion thusCited by: 5.

Vertex algebras, Kac-Moody algebras, and the Monster. Proc Natl. Acad. Sci. USA Vol. 83, pp Richard E. Borcherds, Trinity College, Cambridge CB2 1TQ, England. Communicated by Walter Feit, Decem ABSTRACT It is known that the adjoint representation of any Kac-Moody.

of relative untwisted vertex operators led in [DL2] to three levels of generalization of the concept of vertex operator algebra (and module). One of these notions − that of “generalized vertex operator algebra” − enabled us to clarify the essential equivalence between the Z-algebras of [LP1]-[LP2] and the parafermion algebras of [ZF1.

Vertex operator algebras can be viewed as "complex analogues" of both Lie algebras and associative algebras. 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.

In this paper the (generalized) Jacobi identity for generalized vertex algebras is extended to multi-operator identities. This work is based on the book of Dong and Lepowsky on generalized vertex algebras and relative vertex operators (Dong and Lepowsky, ), on the work of the author on the Jacobi identity for vertex operator algebras in Husu (), Section 1, and on the work in Husu Cited by: 4.

Vertex operators in algebraic topology Andrew Baker Version 24 (14/04/) Introduction This paper is intended for two rather different audiences.

First we aim to provide algebraic topologists with a timely introduction to some of the algebraic ideas associated with vertex operator algebras. Second we try to demonstrate to alge-Author: Andrew Baker.

Vertex (operator) algebras are a fundamental class of algebraic structures that arose in mathematics and physics in the s. These algebras and their representations are deeply related to many directions in mathematics and physics, in particular, the representation theory of the Fischer–Griess Monster simple finite group and the connection with the phenomena of "Monstrous Moonshine" (cf.

Chongying Dong is the author of Generalized Vertex Algebras and Relative Vertex Operators ( avg rating, 0 ratings, 0 reviews, published ), General. James Lepowsky is the author of Introduction to Vertex Operator Algebras and Their Representations ( avg rating, 1 rating, 0 reviews, published ) /5(4).

Abstract. AbstractIn this paper the (generalized) Jacobi identity for generalized vertex algebras is extended to multi-operator identities. This work is based on the book of Dong and Lepowsky on generalized vertex algebras and relative vertex operators (Dong and Lepowsky, ), on the work of the author on the Jacobi identity for vertex operator algebras in Husu (), Section 1, and on the Cited by: 4.

@inproceedings{DongCosetCA, title={Coset constructions and dual pairs for vertex operator algebras}, author={Chongying Dong and Geoffrey Mason}, year={} } Chongying Dong, Geoffrey Mason Published In this paper a general coset construction for an arbitrary vertex operator algebra.

Vertex and Algebras Generalized New Relative Dong: by Operators Vertex Chongying Chongying Vertex Operators Vertex Relative Dong: and by Generalized Algebras New Vertex Operator Algebras and the Monster by Igor Frenkel (English) Hardcover Boo Vertex Operator Algebras - $ For the case of vector spaces graded by an abelian group (with braiding determined by an abelian 3-cocycle following Joyal-Street), this was done by Dong and Lepowsky in their book "Generalized Vertex Algebras and Relative Vertex Operators".

where L(c p, 1, 0) is the usual Virasoro vertex algebra, is what we call the singlet algebra and is the triplet development was continued in works of the authors and others [Abe, CF, Ru] and it eventually led to new developments in vertex algebra example, orbifold theory for LCFT was recently initiated in [] and [].These examples are expected to be instrumental in the future.

Generalized vertex algebras and relative vertex operators. By Chongying Dong and James Lepowsky. Cite. BibTex; Full citation; Topics: Mathematical Physics and Mathematics. Publisher: Springer. Year: Author: Chongying Dong and James Lepowsky.

The structure theory of a class of generalized loop super-Virasoro algebras is studied in this paper. In particular, the derivation algebras, the automorphism groups and the second cohomology groups of generalized loop centerless supper-Virasoro algebras are determined by: 6.

The term "vertex operator" in mathematics refers mainly to certain operators (in a generalized sense of the term) used in physics to describe interactions of physical states at a "vertex" in string theory and its precursor, dual resonance theory; the term refers more specifically to the closely related operators used in mathematics as a powerful tool in many applications, notably, constructing.

We study intertwining operator algebras introduced and constructed by Huang. In the case that the intertwining operator algebras involve intertwining operators among irreducible modules for their vertex operator subalgebras, a number of results on intertwining operator algebras were given in [Y.-Z.

Huang, Generalized rationality and a “Jacobi identity” for intertwining operator algebras Cited by: 4. Logarithmic Tensor Category Theory for Generalized Modules for a Conformal Vertex Algebra, I: Introduction and Strongly Graded Algebras and Their Generalized Modules Generalized Vertex Algebras and Relative Vertex Operators.

Progress in Math., vol. Birkhäuser, Boston () CrossRef zbMATH Google Scholar. Cited by: Hasse-Schmidt Derivations on Grassmann Algebras With Applications to Vertex Operators. Authors: Gatto, Letterio, Salehyan, Parham Free Preview.

Offers a comprehensive approach to advanced topics such as linear ODEs and generalized Wronskians, Schubert calculus for ordinary Grassmannians and vertex operators arising from the representation.

Vertex algebras, W-algebras, and applications - Masahiko Miyamoto Vertex Operator Algebra and Simultaneous Inversion Daniele Valeri Classical W-algebras and generalized Drinfeld.

Vertex Operator Algebras and the Monster, Volume (Pure and Applied Mathemati Vertex Operator Algebras $ Vertex and Algebras Generalized New Relative Dong: by Operators Vertex Chongying Chongying Vertex Operators Vertex Relative Dong: and by Generalized Algebras New.

A new construction of vertex algebras and quasi modules for vertex algebras, Adv. Math. () Nonlocal vertex algebras generated by formal vertex operators, Selecta Mathematica (N.S.) 11 () On certain categories of modules for affine Lie algebras, Math.

() Certain extensions of vertex operator. Shop Vertex Algebras And Th now. Introduction to Vertex Operator Algebras and Th, Lepowsky, James, Introduction to Vertex - $ to Operator Vertex Introduction Algebras Lepowsky, Th, and James, James, and Th, to Algebras Operator Lepowsky, Introduction Vertex.

In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string addition to physical applications, vertex operator algebras have proven useful in purely mathematical contexts such as monstrous moonshine and the geometric Langlands correspondence.

The related notion of vertex algebra was. These vertex operators satisfy some complicated relations, which are then used as the definition of a vertex algebra. In other words, the original example of a vertex algebra was the vertex algebra of an even lattice, and the definition of a vertex algebra was an axiomatization of this example.

Publications. Recent Papers and books. Lecture notes on vertex algebras and quantum vertex algebras, 96 pages on Apfor my graduate course "Math Selected Topics in Algebra: Vertex algebras and quantum vertex algebras," Spring, Subjects Primary: 17B Vertex operators; vertex operator algebras and related structures Secondary: 17B Infinite-dimensional Lie (super)algebras [See also 22E65] 17B Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 17B Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See Author: Michael Roitman.

There are two types of the elliptic quantum algebras: the face type and the vertex type. Here we only consider the face-type elliptic algebra, which can be viewed as the Drinfeld realization of the face-type elliptic quantum y, we can also consider it as the tensor product of the quantum affine algebra and a Heisenberg algebra.

In this section, we will first review the definition Author: Wen-jing Chang, Xiang-mao Ding. For new readers to the area of vertex algebras a lot of machinery is required as a prerequisite before even being able to provide the formal definition.

The aim of this chapter is to introduce the algebraic properties of a vertex algebra as stated in most introductory texts. A more complete treatment of vertex algebra theory can be found in [10 File Size: KB.Talk:Vertex operator algebra.

Jump to navigation Jump to search In the example of a trivial vertex algebra, there is the statement They are transcribed from the book of Victor Kac and you are probably an ipsock of Mathsci31 March (UTC) Checking by Expert.

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