Lepowsky, J. (James)
Overview
Works:  32 works in 197 publications in 2 languages and 3,524 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Honoree, Other, Dedicatee, Contributor 
Classifications:  QA326, 512.55 
Publication Timeline
.
Most widely held works about
J Lepowsky
Most widely held works by
J Lepowsky
Vertex operator algebras and the Monster by
Igor Frenkel(
Book
)
17 editions published between 1988 and 1992 in English and held by 427 WorldCat member libraries worldwide
This work is motivated by and develops connections between several branches of mathematics and physicsthe theories of Lie algebras, finite groups and modular functions in mathematics, and string theory in physics. The first part of the book presents a new mathematical theory of vertex operator algebras, the algebraic counterpart of twodimensional holomorphic conformal quantum field theory. The remaining part constructs the Monster finite simple group as the automorphism group of a very special vertex operator algebra, called the "moonshine module" because of its relevance to "monstrous moonshine."
17 editions published between 1988 and 1992 in English and held by 427 WorldCat member libraries worldwide
This work is motivated by and develops connections between several branches of mathematics and physicsthe theories of Lie algebras, finite groups and modular functions in mathematics, and string theory in physics. The first part of the book presents a new mathematical theory of vertex operator algebras, the algebraic counterpart of twodimensional holomorphic conformal quantum field theory. The remaining part constructs the Monster finite simple group as the automorphism group of a very special vertex operator algebra, called the "moonshine module" because of its relevance to "monstrous moonshine."
Vertex operators in mathematics and physics : proceedings of a conference, November 1017, 1983 by
J Lepowsky(
Book
)
22 editions published in 1985 in English and Undetermined and held by 304 WorldCat member libraries worldwide
James Lepowsky t The search for symmetry in nature has for a long time provided representation theory with perhaps its chief motivation. According to the standard approach of Lie theory, one looks for infinitesimal symmetry  Lie algebras of operators or concrete realizations of abstract Lie algebras. A central theme in this volume is the construction of affine Lie algebras using formal differential operators called vertex operators, which originally appeared in the dualstring theory. Since the precise description of vertex operators, in both mathematical and physical settings, requires a fair amount of notation, we do not attempt it in this introduction. Instead we refer the reader to the papers of Mandelstam, GoddardOlive, LepowskyWilson and FrenkelLepowskyMeurman. We have tried to maintain consistency of terminology and to some extent notation in the articles herein. To help the reader we shall review some of the terminology. We also thought it might be useful to supplement an earlier fairly detailed exposition of ours [37] with a brief historical account of vertex operators in mathematics and their connection with affine algebras. Since we were involved in the development of the subject, the reader should be advised that what follows reflects our own understanding. For another view, see [29].1 t Partially supported by the National Science Foundation through the Mathematical Sciences Research Institute and NSF Grant MCS 8301664. 1 We would like to thank Igor Frenkel for his valuable comments on the first draft of this introduction
22 editions published in 1985 in English and Undetermined and held by 304 WorldCat member libraries worldwide
James Lepowsky t The search for symmetry in nature has for a long time provided representation theory with perhaps its chief motivation. According to the standard approach of Lie theory, one looks for infinitesimal symmetry  Lie algebras of operators or concrete realizations of abstract Lie algebras. A central theme in this volume is the construction of affine Lie algebras using formal differential operators called vertex operators, which originally appeared in the dualstring theory. Since the precise description of vertex operators, in both mathematical and physical settings, requires a fair amount of notation, we do not attempt it in this introduction. Instead we refer the reader to the papers of Mandelstam, GoddardOlive, LepowskyWilson and FrenkelLepowskyMeurman. We have tried to maintain consistency of terminology and to some extent notation in the articles herein. To help the reader we shall review some of the terminology. We also thought it might be useful to supplement an earlier fairly detailed exposition of ours [37] with a brief historical account of vertex operators in mathematics and their connection with affine algebras. Since we were involved in the development of the subject, the reader should be advised that what follows reflects our own understanding. For another view, see [29].1 t Partially supported by the National Science Foundation through the Mathematical Sciences Research Institute and NSF Grant MCS 8301664. 1 We would like to thank Igor Frenkel for his valuable comments on the first draft of this introduction
Generalized vertex algebras and relative vertex operators by
Chongying Dong(
Book
)
13 editions published in 1993 in English and held by 301 WorldCat member libraries worldwide
The rapidlyevolving 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. 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. Dong and Lepowsky have generalized the theory of vertex operator algebras in a systematic way at three successively more general levels, all of which incorporate onedimensional braid groups representations intrinsically into the algebraic structure: First, the notion of "generalized vertex operator algebra" incorporates such structures as Zalgebras, parafermion algebras, and vertex operator superalgebras. Next, what they term "generalized vertex algebras" further encompass the algebras of vertex operators associated with rational lattices. Finally, the most general of the three notions, that of "abelian intertwining algebra," also illuminates the theory of intertwining operator for certain classes of vertex operator algebras. The monograph is written in a n accessible and selfcontained 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
13 editions published in 1993 in English and held by 301 WorldCat member libraries worldwide
The rapidlyevolving 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. 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. Dong and Lepowsky have generalized the theory of vertex operator algebras in a systematic way at three successively more general levels, all of which incorporate onedimensional braid groups representations intrinsically into the algebraic structure: First, the notion of "generalized vertex operator algebra" incorporates such structures as Zalgebras, parafermion algebras, and vertex operator superalgebras. Next, what they term "generalized vertex algebras" further encompass the algebras of vertex operators associated with rational lattices. Finally, the most general of the three notions, that of "abelian intertwining algebra," also illuminates the theory of intertwining operator for certain classes of vertex operator algebras. The monograph is written in a n accessible and selfcontained 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
Functional analysis on the eve of the 21st century by
S. G Gindikin(
Book
)
27 editions published between 1995 and 1996 in English and held by 290 WorldCat member libraries worldwide
These two volumes contain eighteen invited papers by distinguished mathematicians in honor of the eightieth birthday of Israel M. Gelfand, one of the most remarkable mathematicians of our time. Gelfand has played a crucial role in the development of functional analysis during the last halfcentury. His work and his philosophy have in fact helped shape our understanding of the term 'functional analysis'. The papers in these volumes largely concern areas in which Gelfand has a very strong interest today, including geometric quantum field theory, representation theory, combinatorial structures underlying various 'continuous' constructions, quantum groups and geometry. The second of the two volumes contains the somewhat more 'geometric' papers, although such a designation is to a certain extent arbitrary, because of the breadth of the papers
27 editions published between 1995 and 1996 in English and held by 290 WorldCat member libraries worldwide
These two volumes contain eighteen invited papers by distinguished mathematicians in honor of the eightieth birthday of Israel M. Gelfand, one of the most remarkable mathematicians of our time. Gelfand has played a crucial role in the development of functional analysis during the last halfcentury. His work and his philosophy have in fact helped shape our understanding of the term 'functional analysis'. The papers in these volumes largely concern areas in which Gelfand has a very strong interest today, including geometric quantum field theory, representation theory, combinatorial structures underlying various 'continuous' constructions, quantum groups and geometry. The second of the two volumes contains the somewhat more 'geometric' papers, although such a designation is to a certain extent arbitrary, because of the breadth of the papers
Introduction to vertex operator algebras and their representations by
J Lepowsky(
Book
)
11 editions published in 2004 in English and held by 251 WorldCat member libraries worldwide
Vertex operator algebra theory is a new area of mathematics. It has been an exciting and evergrowing subject from the beginning, starting even before R. Borcherds introduced the precise mathematical notion of "vertex algebra" in the 1980s [BI]. Having developed in conjunction with string theory in theoretical physics and with the theory of "monstrous moonshine" and infinitedimensional Lie algebra theory in mathematics, vertex (operator) algebra theory is qualitatively different from traditional algebraic theories, reflecting the "nonclassical" nature of string theory and of monstrous moonshine. The theory has revealed new perspectives that were unavailable without it, and continues to do so. "Monstrous moonshine" began as an astonishing set of conjectures relating the Monster finite simple group to the theory of modular functions in number theory. As is now known, vertex operator algebra theory is a foundational pillar of monstrous moonshine. With the theory available, one can formulate and try to solve new problems that have farreaching implications in a wide range of fields that had not previously been thought of as being related. This book systematically introduces the theory of vertex (operator) algebras from the beginning, using "formal calculus," and takes the reader through the fundamental theory to the detailed construction of examples. The axiomatic foundations of vertex operator algebras and modules are studied in detail, general construction theorems for vertex operator algebras and modules are presented, and the most basic families of vertex operator algebras are constructed and their irreducible modules are constructed and are also classified. The construction theorems for algebras and modules are based on a study of representations of a vertex operator algebra, as opposed to modules for the algebra, as developed in [Li3]. A significant feature of the theory is that in general, the construction of modules for (or representations of) a vertex operator algebra is in some sense more subtle than the construction of the algebra itself. With the body of theory presented in this book as background, the reader will be well prepared to embark on any of a vast range of directions in the theory and its applications
11 editions published in 2004 in English and held by 251 WorldCat member libraries worldwide
Vertex operator algebra theory is a new area of mathematics. It has been an exciting and evergrowing subject from the beginning, starting even before R. Borcherds introduced the precise mathematical notion of "vertex algebra" in the 1980s [BI]. Having developed in conjunction with string theory in theoretical physics and with the theory of "monstrous moonshine" and infinitedimensional Lie algebra theory in mathematics, vertex (operator) algebra theory is qualitatively different from traditional algebraic theories, reflecting the "nonclassical" nature of string theory and of monstrous moonshine. The theory has revealed new perspectives that were unavailable without it, and continues to do so. "Monstrous moonshine" began as an astonishing set of conjectures relating the Monster finite simple group to the theory of modular functions in number theory. As is now known, vertex operator algebra theory is a foundational pillar of monstrous moonshine. With the theory available, one can formulate and try to solve new problems that have farreaching implications in a wide range of fields that had not previously been thought of as being related. This book systematically introduces the theory of vertex (operator) algebras from the beginning, using "formal calculus," and takes the reader through the fundamental theory to the detailed construction of examples. The axiomatic foundations of vertex operator algebras and modules are studied in detail, general construction theorems for vertex operator algebras and modules are presented, and the most basic families of vertex operator algebras are constructed and their irreducible modules are constructed and are also classified. The construction theorems for algebras and modules are based on a study of representations of a vertex operator algebra, as opposed to modules for the algebra, as developed in [Li3]. A significant feature of the theory is that in general, the construction of modules for (or representations of) a vertex operator algebra is in some sense more subtle than the construction of the algebra itself. With the body of theory presented in this book as background, the reader will be well prepared to embark on any of a vast range of directions in the theory and its applications
On axiomatic approaches to vertex operator algebras and modules by
Igor Frenkel(
Book
)
12 editions published in 1993 in English and Italian and held by 250 WorldCat member libraries worldwide
12 editions published in 1993 in English and Italian and held by 250 WorldCat member libraries worldwide
Structure of the standard modules for the affine Lie algebra A₁ superscript (1) by
J Lepowsky(
Book
)
3 editions published in 1985 in English and held by 196 WorldCat member libraries worldwide
3 editions published in 1985 in English and held by 196 WorldCat member libraries worldwide
Moonshine : the first quarter century and beyond : proceedings of a workshop on the moonshine conjectures and vertex algebras(
Book
)
16 editions published in 2010 in English and held by 196 WorldCat member libraries worldwide
"Modular Tensor Categories (MTCs for short)[1, 16] have attracted much attentionin recent years, which is due to the recognition of their importance in bothpure mathematics  3dimensional topology, representations of Vertex OperatorAlgebras (VOAs for short)  and theoretical physics"Provided by publisher
16 editions published in 2010 in English and held by 196 WorldCat member libraries worldwide
"Modular Tensor Categories (MTCs for short)[1, 16] have attracted much attentionin recent years, which is due to the recognition of their importance in bothpure mathematics  3dimensional topology, representations of Vertex OperatorAlgebras (VOAs for short)  and theoretical physics"Provided by publisher
Lie algebras, vertex operator algebras and their applications : international conference in honor of James Lepowsky and Robert
Wilson on their sixtieth birthdays, May 1721, 2005, North Carolina State University, Raleigh, North Carolina(
Book
)
10 editions published between 2007 and 2008 in English and held by 185 WorldCat member libraries worldwide
10 editions published between 2007 and 2008 in English and held by 185 WorldCat member libraries worldwide
The Gelfand mathematical seminars : 19901992 by
I. M Gelʹfand(
Book
)
23 editions published between 1993 and 1996 in English and Italian and held by 165 WorldCat member libraries worldwide
This Seminar began in Moscow in November 1943 and has continued without interruption up to the present. We are happy that with this vol ume, Birkhiiuser has begun to publish papers of talks from the Seminar. It was, unfortunately, difficult to organize their publication before 1990. Since 1990, most of the talks have taken place at Rutgers University in New Brunswick, New Jersey. Parallel seminars were also held in Moscow, and during July, 1992, at IRES in BuressurYvette, France. Speakers were invited to submit papers in their own style, and to elaborate on what they discussed in the Seminar. We hope that readers will find the diversity of styles appealing, and recognize that to some extent this reflects the diversity of styles in a mathematical society. The principal aim was to have interesting talks, even if the topic was not especially popular at the time. The papers listed in the Table of Contents reflect some of the rich variety of ideas presented in the Seminar. Not all the speakers submit ted papers. Among the interesting talks that influenced the seminar in an important way, let us mention, for example, that of R. Langlands on per colation theory and those of J. Conway and J. McKay on sporadic groups. In addition, there were many extemporaneous talks as well as short discus sions
23 editions published between 1993 and 1996 in English and Italian and held by 165 WorldCat member libraries worldwide
This Seminar began in Moscow in November 1943 and has continued without interruption up to the present. We are happy that with this vol ume, Birkhiiuser has begun to publish papers of talks from the Seminar. It was, unfortunately, difficult to organize their publication before 1990. Since 1990, most of the talks have taken place at Rutgers University in New Brunswick, New Jersey. Parallel seminars were also held in Moscow, and during July, 1992, at IRES in BuressurYvette, France. Speakers were invited to submit papers in their own style, and to elaborate on what they discussed in the Seminar. We hope that readers will find the diversity of styles appealing, and recognize that to some extent this reflects the diversity of styles in a mathematical society. The principal aim was to have interesting talks, even if the topic was not especially popular at the time. The papers listed in the Table of Contents reflect some of the rich variety of ideas presented in the Seminar. Not all the speakers submit ted papers. Among the interesting talks that influenced the seminar in an important way, let us mention, for example, that of R. Langlands on per colation theory and those of J. Conway and J. McKay on sporadic groups. In addition, there were many extemporaneous talks as well as short discus sions
Elementary Lie algebra theory by
J Lepowsky(
Book
)
8 editions published in 1974 in English and Undetermined and held by 51 WorldCat member libraries worldwide
8 editions published in 1974 in English and Undetermined and held by 51 WorldCat member libraries worldwide
Structure of the standard modules for the affine Lie algebra A(1)1 by
J Lepowsky(
Book
)
14 editions published in 1985 in English and held by 36 WorldCat member libraries worldwide
14 editions published in 1985 in English and held by 36 WorldCat member libraries worldwide
Introduction to vertex operator algebras and their representations by
J Lepowsky(
)
1 edition published in 2004 in English and held by 7 WorldCat member libraries worldwide
1 edition published in 2004 in English and held by 7 WorldCat member libraries worldwide
Functional analysis on the eve of the 21st century in honor of the 80th birthday of I.M. Gelfand(
Book
)
in English and held by 4 WorldCat member libraries worldwide
in English and held by 4 WorldCat member libraries worldwide
[Mathematical seminars] by Gelfand Mathematical Seminars(
Book
)
1 edition published in 1996 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1996 in English and held by 2 WorldCat member libraries worldwide
Structure of the standard modules for the Affine Lie algebra A subscript 1 superscript(1) by
Calif.) Mathematical Sciences Research Institute (Berkeley(
Book
)
1 edition published in 1985 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1985 in English and held by 2 WorldCat member libraries worldwide
Vertex operators in mathematical physics : proceedings of a conference, Nov. 10  17, 1983(
Book
)
1 edition published in 1985 in Undetermined and held by 1 WorldCat member library worldwide
1 edition published in 1985 in Undetermined and held by 1 WorldCat member library worldwide
Representations of semisimple Lie groups and an enveloping algebra decomposition by
J Lepowsky(
)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
On axiomatic approaches to vertex operator algebras and modules by
Igor Frenkel(
)
1 edition published in 1993 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 1993 in English and held by 0 WorldCat member libraries worldwide
Encyclopaedia of mathematics. Supplement III by
Shreeram Shankar Abhyankar(
)
1 edition published in 2002 in English and held by 0 WorldCat member libraries worldwide
This is the third supplementary volume to Kluwer's highly acclaimed twelvevolume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and uptodate Encyclopaedia of Mathematics available
1 edition published in 2002 in English and held by 0 WorldCat member libraries worldwide
This is the third supplementary volume to Kluwer's highly acclaimed twelvevolume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and uptodate Encyclopaedia of Mathematics available
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Related Identities
 Frenkel, Igor Author
 Wilson, Robert L. 1946 Other Dedicatee Editor
 Meurman, Arne
 Gelʹfand, I. M. (Izrailʹ Moiseevich) Other Honoree Dedicatee Author Editor
 Huang, YiZhi 1959 Contributor Editor
 Gindikin, S. G. (Semen Grigorʹevich) Other Author Editor
 Dong, Chongying 1958 Author
 Mandelstam, Stanley Editor
 Singer, I. M. (Isadore Manuel) 1924 Editor
 Li, Haisheng 1962
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Associated Subjects
Algebra Finite groups Functional analysis Geometry Group theory Lie algebras Mathematics MathematicsCongresses Modular functions Modules (Algebra) Nonassociative algebras Operator theory Physics Quantum field theory Representations of algebras Superstring theories Topological groups Topology Vertex operator algebras
Alternative Names
James Ivan Lepowsky USamerikanischer Mathematiker
James Lepowsky Amerikaans wiskundige
James Lepowsky amerikansk matematikar
James Lepowsky amerikansk matematiker
James Lepowsky matemático estadounidense
James Lepowsky matematico statunitense
James Lepowsky mathématicien américain
Lepowsky, J.
Lepowsky, J. 1944
Lepowsky, James
Lepowsky, James I. 1944
Lepowsky, James Ivan 1944
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