Lepowsky, J. (James)
Overview
Works:  59 works in 235 publications in 2 languages and 4,414 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Other, Honoree, Dedicatee 
Classifications:  QA326, 512.55 
Publication Timeline
.
Most widely held works about
J Lepowsky
 Lie algebras, vertex operator algebras, and related topics : a conference in honor of J. Lepowsky and R. Wilson on Lie algebras, vertex operator algebras, and related topics, August 1418, 2015, University of Notre Dame, Notre Dame, IN by Vertex Operator Algebras, and Related Topics Conference in Honor of J. Lepowsky and R. Wilson on Lie Algebras( )
Most widely held works by
J Lepowsky
Moonshine : the first quarter century and beyond : proceedings of a workshop on the moonshine conjectures and vertex algebras(
)
17 editions published in 2010 in English and held by 816 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"Résumé de l'éditeur
17 editions published in 2010 in English and held by 816 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"Résumé de l'éditeur
Vertex operator algebras and the Monster by
Igor Frenkel(
Book
)
19 editions published between 1988 and 2014 in English and held by 634 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."
19 editions published between 1988 and 2014 in English and held by 634 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."
Generalized vertex algebras and relative vertex operators by
Chongying Dong(
Book
)
12 editions published in 1993 in English and held by 378 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
12 editions published in 1993 in English and held by 378 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
Vertex operators in mathematics and physics : proceedings of a conference, November 1017, 1983 by
J Lepowsky(
Book
)
21 editions published in 1985 in English and held by 375 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
21 editions published in 1985 in English and held by 375 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
Introduction to vertex operator algebras and their representations by
J Lepowsky(
Book
)
13 editions published between 2004 and 2010 in English and held by 330 WorldCat member libraries worldwide
"Requiring only a familiarity with basic algebra, Introduction to Vertex Operator Algebras and Their Representations will be useful for graduate students and researchers in mathematics and physics. The book's selfcontained presentation of the core topics will equip readers to embark on many active research direction related to vertex operator algebras, group theory, representation theory, and string theory."Jacket
13 editions published between 2004 and 2010 in English and held by 330 WorldCat member libraries worldwide
"Requiring only a familiarity with basic algebra, Introduction to Vertex Operator Algebras and Their Representations will be useful for graduate students and researchers in mathematics and physics. The book's selfcontained presentation of the core topics will equip readers to embark on many active research direction related to vertex operator algebras, group theory, representation theory, and string theory."Jacket
On axiomatic approaches to vertex operator algebras and modules by
Igor Frenkel(
Book
)
14 editions published between 1993 and 2014 in English and Italian and held by 304 WorldCat member libraries worldwide
The basic definitions and properties of vertex operator algebras, modules, intertwining operators and related concepts are presented, following a fundamental analogy with Lie algebra theory. The first steps in the development of the general theory are taken, and various natural and useful reformulations of the axioms are given. In particular, tensor products of algebras and modules, adjoint vertex operators and contragradient modules, adjoint intertwining operators and fusion rules are studied in greater depth. This paper lays the monodromyfree axiomatic foundation of the general theory of vertex operator algebras, modules and intertwining operators
14 editions published between 1993 and 2014 in English and Italian and held by 304 WorldCat member libraries worldwide
The basic definitions and properties of vertex operator algebras, modules, intertwining operators and related concepts are presented, following a fundamental analogy with Lie algebra theory. The first steps in the development of the general theory are taken, and various natural and useful reformulations of the axioms are given. In particular, tensor products of algebras and modules, adjoint vertex operators and contragradient modules, adjoint intertwining operators and fusion rules are studied in greater depth. This paper lays the monodromyfree axiomatic foundation of the general theory of vertex operator algebras, modules and intertwining operators
The Gelfand mathematical seminars : 19901992 by
I. M Gelʹfand(
)
23 editions published between 1993 and 1996 in 3 languages and held by 298 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 3 languages and held by 298 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
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 225 WorldCat member libraries worldwide
3 editions published in 1985 in English and held by 225 WorldCat member libraries worldwide
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
)
12 editions published between 2007 and 2012 in English and held by 201 WorldCat member libraries worldwide
12 editions published between 2007 and 2012 in English and held by 201 WorldCat member libraries worldwide
Functional analysis on the eve of the 21st century(
Book
)
4 editions published in 1995 in English and held by 189 WorldCat member libraries worldwide
4 editions published in 1995 in English and held by 189 WorldCat member libraries worldwide
Functional analysis on the eve of the 21st century in honor of the eightieth birthday of I.M. Gelfand by
S. G Gindikin(
)
17 editions published between 1995 and 1996 in English and held by 136 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
17 editions published between 1995 and 1996 in English and held by 136 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
Encyclopaedia of Mathematics, Supplement III by
Shreeram Shankar Abhyankar(
)
1 edition published in 2002 in English and held by 114 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 114 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
Lie algebras, vertex operator algebras, and related topics : a conference in honor of J. Lepowsky and R. Wilson on Lie algebras,
vertex operator algebras, and related topics, August 1418, 2015, University of Notre Dame, Notre Dame, IN by Vertex Operator Algebras, and Related Topics Conference in Honor of J. Lepowsky and R. Wilson on Lie Algebras(
Book
)
5 editions published in 2017 in English and held by 69 WorldCat member libraries worldwide
5 editions published in 2017 in English and held by 69 WorldCat member libraries worldwide
Functional Analysis on the Eve of the 21st Century Volume II : In Honor of the Eightieth Birthday of I.M. Gelfand by
S. G Gindikin(
)
1 edition published in 1996 in English and held by 60 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
1 edition published in 1996 in English and held by 60 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
Elementary Lie algebra theory by
J Lepowsky(
Book
)
9 editions published in 1974 in English and Undetermined and held by 57 WorldCat member libraries worldwide
9 editions published in 1974 in English and Undetermined and held by 57 WorldCat member libraries worldwide
Functional analysis on the eve of the 21st century : in honor of the eightieth birthday of I.M. Gelfand(
Book
)
8 editions published between 1995 and 1996 in English and held by 37 WorldCat member libraries worldwide
8 editions published between 1995 and 1996 in English and held by 37 WorldCat member libraries worldwide
Vertex operator algebras and the Monster by
Igor Frenkel(
)
1 edition published in 1988 in English and held by 27 WorldCat member libraries worldwide
1 edition published in 1988 in English and held by 27 WorldCat member libraries worldwide
Structure of the standard modules for the affine Lie algebra A [superscript (1)] by
J Lepowsky(
Book
)
3 editions published in 1985 in English and held by 13 WorldCat member libraries worldwide
3 editions published in 1985 in English and held by 13 WorldCat member libraries worldwide
Structure of the standard modules for the affine Lie algebra A(1)1 by
J Lepowsky(
Book
)
1 edition published in 1985 in English and held by 13 WorldCat member libraries worldwide
1 edition published in 1985 in English and held by 13 WorldCat member libraries worldwide
Functional analysis on the eve of the 21st century(
Book
)
1 edition published in 1995 in English and held by 11 WorldCat member libraries worldwide
1 edition published in 1995 in English and held by 11 WorldCat member libraries worldwide
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Kids  General  Special 
Related Identities
 Frenkel, Igor Author
 Tuite, Michael P. Editor
 McKay, John 1939 Editor
 Meurman, Arne Other
 Wilson, Robert L. 1946 Other Honoree Dedicatee Editor
 Gelʹfand, I. M. (Izrailʹ Moiseevich) Other Honoree Dedicatee Author Editor
 Huang, YiZhi 1959 Editor
 Gindikin, S. G. (Semen Grigorʹevich) Other Author Editor
 Dong, Chongying 1958 Author
 Mandelstam, Stanley Editor
Useful Links
Associated Subjects
Algebra Finite groups Functional analysis Gelʹfand, I. M.(Izrailʹ Moiseevich) 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
Covers
Alternative Names
James Ivan Lepowsky USamerikanischer Mathematiker
James Lepowsky Amerikaans wiskundige
James Lepowsky amerikansk matematikar
James Lepowsky amerikansk matematiker
James Lepowsky matemàtic estatunidenc
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
ジェームズ・レポウスキー
詹姆斯·雷保斯基
Languages