Kac, Victor G. 1943
Overview
Works:  54 works in 268 publications in 4 languages and 5,402 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Other 
Classifications:  QA252.3, 512.55 
Publication Timeline
.
Most widely held works by
Victor G Kac
Bombay lectures on highest weight representations of infinite dimensional lie algebras by
Victor G Kac(
)
26 editions published between 1987 and 2013 in English and held by 1,832 WorldCat member libraries worldwide
The second edition of this book incorporates, as its first part, the largely unchanged text of the first edition, while its second part is the collection of lectures on vertex algebras, delivered by Professor Kac at the TIFR in January 2003. The basic idea of these lectures was to demonstrate how the key notions of the theory of vertex algebrassuch as quantum fields, their normal ordered product and lambdabracket, energymomentum field and conformal weight, untwisted and twisted representationssimplify and clarify the constructions of the first edition of the book.  Cover
26 editions published between 1987 and 2013 in English and held by 1,832 WorldCat member libraries worldwide
The second edition of this book incorporates, as its first part, the largely unchanged text of the first edition, while its second part is the collection of lectures on vertex algebras, delivered by Professor Kac at the TIFR in January 2003. The basic idea of these lectures was to demonstrate how the key notions of the theory of vertex algebrassuch as quantum fields, their normal ordered product and lambdabracket, energymomentum field and conformal weight, untwisted and twisted representationssimplify and clarify the constructions of the first edition of the book.  Cover
Infinite dimensional Lie algebras by
Victor G Kac(
Book
)
67 editions published between 1982 and 2014 in 3 languages and held by 1,146 WorldCat member libraries worldwide
The third, substantially revised edition of a monograph concerned with KacMoody algebras, a particular class of infinitedimensional Lie albegras, and their representations, based on courses given over a number of years at MIT and in Paris
67 editions published between 1982 and 2014 in 3 languages and held by 1,146 WorldCat member libraries worldwide
The third, substantially revised edition of a monograph concerned with KacMoody algebras, a particular class of infinitedimensional Lie albegras, and their representations, based on courses given over a number of years at MIT and in Paris
Quantum calculus by
Victor G Kac(
Book
)
18 editions published between 2001 and 2011 in English and held by 436 WorldCat member libraries worldwide
Simply put, quantum calculus is ordinary calculus without taking limits. This undergraduate text develops two types of quantum calculi, the qcalculus and the hcalculus. As this book develops quantum calculus along the lines of traditional calculus, the reader discovers, with a remarkable inevitability, many important notions and results of classical mathematics. This book is written at the level of a first course in calculus and linear algebra and is aimed at undergraduate and beginning graduate students in mathematics, computer science, and physics. It is based on lectures and seminars given by Professor Kac over the last few years at MIT. Victor Kac is Professor of Mathematics at MIT. He is an author of 4 books and over a hundred research papers. He was awarded the Wigner Medal for his work on KacMoody algebras that has numerous applications to mathematics and theoretical physics. He is a honorary member of the Moscow Mathematical Society. Pokman Cheung graduated from MIT in 2001 after three years of undergraduate studies. He is presently a graduate student at Stanford University
18 editions published between 2001 and 2011 in English and held by 436 WorldCat member libraries worldwide
Simply put, quantum calculus is ordinary calculus without taking limits. This undergraduate text develops two types of quantum calculi, the qcalculus and the hcalculus. As this book develops quantum calculus along the lines of traditional calculus, the reader discovers, with a remarkable inevitability, many important notions and results of classical mathematics. This book is written at the level of a first course in calculus and linear algebra and is aimed at undergraduate and beginning graduate students in mathematics, computer science, and physics. It is based on lectures and seminars given by Professor Kac over the last few years at MIT. Victor Kac is Professor of Mathematics at MIT. He is an author of 4 books and over a hundred research papers. He was awarded the Wigner Medal for his work on KacMoody algebras that has numerous applications to mathematics and theoretical physics. He is a honorary member of the Moscow Mathematical Society. Pokman Cheung graduated from MIT in 2001 after three years of undergraduate studies. He is presently a graduate student at Stanford University
Infinite dimensional groups with applications by
Victor G Kac(
Book
)
15 editions published in 1985 in English and held by 346 WorldCat member libraries worldwide
15 editions published in 1985 in English and held by 346 WorldCat member libraries worldwide
Vertex algebras for beginners by
Victor G Kac(
Book
)
32 editions published between 1996 and 2001 in English and held by 345 WorldCat member libraries worldwide
Vertex Algebras introduces the algebraic aspects of conformal field theory and provides access to many unusual mathematical notions
32 editions published between 1996 and 2001 in English and held by 345 WorldCat member libraries worldwide
Vertex Algebras introduces the algebraic aspects of conformal field theory and provides access to many unusual mathematical notions
Graded simple Jordan superalgebras of growth one by
Victor G Kac(
Book
)
11 editions published in 2001 in English and held by 263 WorldCat member libraries worldwide
Introduction Structure of the even part Cartan type Even part is direct sum of two loop algebras $A$ is a loop algebra $J$ is a finite dimensional Jordan superalgebra or a Jordan superalgebra of a superform The main case Impossible cases Bibliography
11 editions published in 2001 in English and held by 263 WorldCat member libraries worldwide
Introduction Structure of the even part Cartan type Even part is direct sum of two loop algebras $A$ is a loop algebra $J$ is a finite dimensional Jordan superalgebra or a Jordan superalgebra of a superform The main case Impossible cases Bibliography
Vertex algebras for beginners by
Victor G Kac(
Book
)
2 editions published in 1998 in English and held by 222 WorldCat member libraries worldwide
2 editions published in 1998 in English and held by 222 WorldCat member libraries worldwide
Lie groups, geometry, and representation theory : a tribute to the life and work of Bertram Kostant(
)
12 editions published in 2018 in English and held by 218 WorldCat member libraries worldwide
"This volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928  February 2, 2017), is a collection of 19 invited papers by leading mathematicians working in Lie theory, representation theory, algebra, geometry, and mathematical physics. Kostant's fundamental work in all of these areas has provided deep new insights and connections, and has created new fields of research. It features important recent results of the contributors with full details of their proofs."
12 editions published in 2018 in English and held by 218 WorldCat member libraries worldwide
"This volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928  February 2, 2017), is a collection of 19 invited papers by leading mathematicians working in Lie theory, representation theory, algebra, geometry, and mathematical physics. Kostant's fundamental work in all of these areas has provided deep new insights and connections, and has created new fields of research. It features important recent results of the contributors with full details of their proofs."
Infinite dimensional lie algebras and groups : proceedings of the conference held at CIRM, Luminy, Marseille, July 48, 1988 by
Victor G Kac(
Book
)
18 editions published between 1989 and 1990 in English and held by 203 WorldCat member libraries worldwide
"Readership: Mathematicians and mathematical physicists."
18 editions published between 1989 and 1990 in English and held by 203 WorldCat member libraries worldwide
"Readership: Mathematicians and mathematical physicists."
Symmetries, Differential Equations and Applications : SDEAIII, İstanbul, Turkey, August 2017 by Differential Equations and Applications International Conference on Symmetries(
)
9 editions published between 2018 and 2019 in English and held by 182 WorldCat member libraries worldwide
Based on the third International Conference on Symmetries, Differential Equations and Applications (SDEAIII), this proceedings volume highlights recent important advances and trends in the applications of Lie groups, including a broad area of topics in interdisciplinary studies, ranging from mathematical physics to financial mathematics. The selected and peerreviewed contributions gathered here cover Lie theory and symmetry methods in differential equations, Lie algebras and Lie pseudogroups, supersymmetry and superintegrability, representation theory of Lie algebras, classification problems, conservation laws, and geometrical methods. The SDEA III, held in honour of the Centenary of Noether's Theorem, proven by the prominent German mathematician Emmy Noether, at Istanbul Technical University in August 2017 provided a productive forum for academic researchers, both junior and senior, and students to discuss and share the latest developments in the theory and applications of Lie symmetry groups. This work has an interdisciplinary appeal and will be a valuable read for researchers in mathematics, mechanics, physics, engineering, medicine and finance
9 editions published between 2018 and 2019 in English and held by 182 WorldCat member libraries worldwide
Based on the third International Conference on Symmetries, Differential Equations and Applications (SDEAIII), this proceedings volume highlights recent important advances and trends in the applications of Lie groups, including a broad area of topics in interdisciplinary studies, ranging from mathematical physics to financial mathematics. The selected and peerreviewed contributions gathered here cover Lie theory and symmetry methods in differential equations, Lie algebras and Lie pseudogroups, supersymmetry and superintegrability, representation theory of Lie algebras, classification problems, conservation laws, and geometrical methods. The SDEA III, held in honour of the Centenary of Noether's Theorem, proven by the prominent German mathematician Emmy Noether, at Istanbul Technical University in August 2017 provided a productive forum for academic researchers, both junior and senior, and students to discuss and share the latest developments in the theory and applications of Lie symmetry groups. This work has an interdisciplinary appeal and will be a valuable read for researchers in mathematics, mechanics, physics, engineering, medicine and finance
Infinite Dimensional Groups with Applications by
Victor G Kac(
)
1 edition published in 1985 in English and held by 59 WorldCat member libraries worldwide
This volume records most of the talks given at the Conference on Infinitedimensional Groups held at the Mathematical Sciences Research Institute at Berkeley, California, May 10May 15, 1984, as a part of the special program on KacMoody Lie algebras. The purpose of the conference was to review recent developments of the theory of infinitedimensional groups and its applications. The present collection concentrates on three very active, interrelated directions of the field: general KacMoody groups, gauge groups (especially loop groups) and diffeomorphism groups. I would like to express my thanks to the MSRI for sponsoring the meeting, to Ms. Faye Yeager for excellent typing, to the authors for their manuscripts, and to SpringerVerlag for publishing this volume. V. Kac INFINITE DIMENSIONAL GROUPS WITH APPLICATIONS CONTENTS The Lie Group Structure of M. Adams. T. Ratiu 1 Diffeomorphism Groups and & R. Schmid Invertible Fourier Integral Operators with Applications On LandauLifshitz Equation and E. Date 71 Infinite Dimensional Groups Flat Manifolds and Infinite D.S. Freed 83 Dimensional Kahler Geometry PositiveEnergy Representations R. Goodman 125 of the Group of Diffeomorphisms of the Circle Instantons and Harmonic Maps M.A. Guest 137 A Coxeter Group Approach to Z. Haddad 157 Schubert Varieties Constructing Groups Associated to V.G. Kac 167 InfiniteDimensional Lie Algebras I. Kaplansky 217 HarishChandra Modules Over the Virasoro Algebra & L.J. Santharoubane 233 Rational Homotopy Theory of Flag S
1 edition published in 1985 in English and held by 59 WorldCat member libraries worldwide
This volume records most of the talks given at the Conference on Infinitedimensional Groups held at the Mathematical Sciences Research Institute at Berkeley, California, May 10May 15, 1984, as a part of the special program on KacMoody Lie algebras. The purpose of the conference was to review recent developments of the theory of infinitedimensional groups and its applications. The present collection concentrates on three very active, interrelated directions of the field: general KacMoody groups, gauge groups (especially loop groups) and diffeomorphism groups. I would like to express my thanks to the MSRI for sponsoring the meeting, to Ms. Faye Yeager for excellent typing, to the authors for their manuscripts, and to SpringerVerlag for publishing this volume. V. Kac INFINITE DIMENSIONAL GROUPS WITH APPLICATIONS CONTENTS The Lie Group Structure of M. Adams. T. Ratiu 1 Diffeomorphism Groups and & R. Schmid Invertible Fourier Integral Operators with Applications On LandauLifshitz Equation and E. Date 71 Infinite Dimensional Groups Flat Manifolds and Infinite D.S. Freed 83 Dimensional Kahler Geometry PositiveEnergy Representations R. Goodman 125 of the Group of Diffeomorphisms of the Circle Instantons and Harmonic Maps M.A. Guest 137 A Coxeter Group Approach to Z. Haddad 157 Schubert Varieties Constructing Groups Associated to V.G. Kac 167 InfiniteDimensional Lie Algebras I. Kaplansky 217 HarishChandra Modules Over the Virasoro Algebra & L.J. Santharoubane 233 Rational Homotopy Theory of Flag S
Algebras, Representations and Applications by
V Futorny(
)
1 edition published in 2009 in English and held by 40 WorldCat member libraries worldwide
1 edition published in 2009 in English and held by 40 WorldCat member libraries worldwide
Infinite dimensional Lie algebras : an introd by
Victor G Kac(
Book
)
4 editions published between 1983 and 1995 in 3 languages and held by 25 WorldCat member libraries worldwide
4 editions published between 1983 and 1995 in 3 languages and held by 25 WorldCat member libraries worldwide
Bombay Lectures on highest weight representations of infinite dimensional lie algebras by
Victor G Kac(
Book
)
2 editions published in 2013 in English and held by 13 WorldCat member libraries worldwide
2 editions published in 2013 in English and held by 13 WorldCat member libraries worldwide
Infinite dimensional groups with applications(
Book
)
1 edition published in 1985 in English and held by 11 WorldCat member libraries worldwide
1 edition published in 1985 in English and held by 11 WorldCat member libraries worldwide
Bombay lectures on highest weight representations of infinite dimensional Lie algebras by
Victor G Kac(
)
2 editions published between 1987 and 2013 in English and held by 10 WorldCat member libraries worldwide
To mathematicians, it illustrates the interaction of the key ideas of the representation theory of infinite dimensional Lie algebras and of the theory of vertex algebras; and to physicists, these theories are turning into an important component of such domains of theoretical physics as soliton theory, conformal field theory, the theory of twodimensional statistical models, and string theory
2 editions published between 1987 and 2013 in English and held by 10 WorldCat member libraries worldwide
To mathematicians, it illustrates the interaction of the key ideas of the representation theory of infinite dimensional Lie algebras and of the theory of vertex algebras; and to physicists, these theories are turning into an important component of such domains of theoretical physics as soliton theory, conformal field theory, the theory of twodimensional statistical models, and string theory
Lie theory and geometry : in honor of Bertram Kostant by
J.L Brylinski(
)
2 editions published in 1994 in English and held by 6 WorldCat member libraries worldwide
This volume, dedicated to Bertram Kostant on the occasion of his 65th birthday, is a collection of 22 invited papers by leading mathematicians working in Lie theory, geometry, algebra, and mathematical physics. Kostant's fundamental work in all these areas has provided deep new insights and connections, and has created new fields of research. The papers gathered here present original research articles as well as expository papers, broadly reflecting the range of Kostant's work
2 editions published in 1994 in English and held by 6 WorldCat member libraries worldwide
This volume, dedicated to Bertram Kostant on the occasion of his 65th birthday, is a collection of 22 invited papers by leading mathematicians working in Lie theory, geometry, algebra, and mathematical physics. Kostant's fundamental work in all these areas has provided deep new insights and connections, and has created new fields of research. The papers gathered here present original research articles as well as expository papers, broadly reflecting the range of Kostant's work
Beskonechnomernye algebry Li by
Victor G Kac(
Book
)
2 editions published in 1993 in Russian and held by 3 WorldCat member libraries worldwide
2 editions published in 1993 in Russian and held by 3 WorldCat member libraries worldwide
Ėkonomičeskoe sorevnovanie meždu S[ojuzom] SSR i SŠA(
Book
)
1 edition published in 1959 in Undetermined and held by 3 WorldCat member libraries worldwide
1 edition published in 1959 in Undetermined and held by 3 WorldCat member libraries worldwide
Cyclic elements in semisimple Lie algebras by A. G Elashvili(
)
1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide
We develop a theory of cyclic elements associated with nilpotent elements in semisimple Lie algebras. This notion was introduced by Kostant, who associated a cycic element with the principal nilpotent and proved that it is semisimple. In particular, we classify all nilpotents giving rise to semisimple and to nilpotent cyclic elements. As an application, we obtain an explicit construction of all regular elements in the Weyl groups
1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide
We develop a theory of cyclic elements associated with nilpotent elements in semisimple Lie algebras. This notion was introduced by Kostant, who associated a cycic element with the principal nilpotent and proved that it is semisimple. In particular, we classify all nilpotents giving rise to semisimple and to nilpotent cyclic elements. As an application, we obtain an explicit construction of all regular elements in the Weyl groups
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Related Identities
 Raina, A. K. Other Contributor
 Rozhkovskaya, Natasha Other Author Contributor
 Cheung, Pokman Author
 Mathematical Sciences Research Institute (Berkeley, Calif.)
 Zelmanov, Efim 1955
 Martinez, C. (Consuelo) 1955
 Popov, V. L. (Vladimir Leonidovich) Editor
 Kostant, Bertram Honoree Dedicatee
 Winternitz, Pavel Editor
 Özer, Teoman Editor
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Associated Subjects
Algebra Algebras, Linear Calculus Combinatorial analysis Differentiable dynamical systems Differential equations Functional equations Geometry Geometry, Algebraic Geometry, Differential Global analysis (Mathematics) Global differential geometry Group theory Infinite dimensional Lie algebras Jordan algebras Lie algebras Lie groups Mathematical physics Mathematics Number theory Quantum field theory Quantum theory Representations of algebras Representations of groups Representations of Lie groups Superalgebras Topological groups Topology Vertex operator algebras
Covers
Alternative Names
Kac, V.
Kac, V. 1943
Kac, V.G.
Kac, V. G. 1943
Kac, V. (Victor), 1943
Kac, Victor.
Kac, Victor 1943
Kac, Victor G.
Kac, Victor Gershevich
Kac, Victor Grigorievich
Victor Kac matemàtic rus
Victor Kac matemático ruso
Victor Kac matemáticu estauxunidense
Victor Kac mathématicien américain
Victor Kac Russian mathematician
Victor Kac Russisch wiskundige
Victor Kac USamerikanischer Mathematiker
Viktor Kac Rusa matematikisto
Виктор Кац советский и американский математик
Віктор Кац
Кац, Виктор Гершевич, 1943....
Кац, Виктор советский и американский математик
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