Kac, Victor G. 1943
Overview
Works:  35 works in 216 publications in 3 languages and 4,578 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
Infinite dimensional Lie algebras by
Victor G Kac(
Book
)
63 editions published between 1982 and 2014 in 4 languages and held by 1,031 WorldCat member libraries worldwide
63 editions published between 1982 and 2014 in 4 languages and held by 1,031 WorldCat member libraries worldwide
Vertex algebras for beginners by
Victor G Kac(
Book
)
28 editions published between 1996 and 2001 in English and held by 520 WorldCat member libraries worldwide
28 editions published between 1996 and 2001 in English and held by 520 WorldCat member libraries worldwide
Quantum calculus by
Victor G Kac(
Book
)
17 editions published between 2001 and 2011 in English and held by 358 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
17 editions published between 2001 and 2011 in English and held by 358 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
)
14 editions published in 1985 in English and held by 350 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
14 editions published in 1985 in English and held by 350 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
Bombay lectures on highest weight representations of infinite dimensional lie algebras by
Victor G Kac(
Book
)
30 editions published between 1987 and 2013 in English and held by 325 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
30 editions published between 1987 and 2013 in English and held by 325 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
Graded simple Jordan superalgebras of growth one by
Victor G Kac(
Book
)
13 editions published in 2001 in English and held by 229 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
13 editions published in 2001 in English and held by 229 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
Infinite dimensional lie algebras and groups : proceedings of the conference held at CIRM, Luminy, Marseille, July 48, 1988 by
Victor G Kac(
Book
)
16 editions published in 1989 in English and held by 168 WorldCat member libraries worldwide
"Readership: Mathematicians and mathematical physicists."
16 editions published in 1989 in English and held by 168 WorldCat member libraries worldwide
"Readership: Mathematicians and mathematical physicists."
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
Characters and fusion rules for Walgebras via quantized DrinfeldSokolov reductions by
Edward Frenkel(
Book
)
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
Abstract: "Using the cohomological approach to Walgebras, we calculate characters and fusion coefficients for their representations obtained from modular invariant representations of affine algebras by the quantized DrinfeldSokolov reduction."
2 editions published in 1992 in English and held by 3 WorldCat member libraries worldwide
Abstract: "Using the cohomological approach to Walgebras, we calculate characters and fusion coefficients for their representations obtained from modular invariant representations of affine algebras by the quantized DrinfeldSokolov reduction."
Torsion in cohomology of compact Lie groups by
Victor G Kac(
Book
)
1 edition published in 1984 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1984 in English and held by 2 WorldCat member libraries worldwide
Representations of quantum groups at roots of 1 : reduction to the exceptional case by
Corrado De Concini(
Book
)
2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide
Structure of some categories of representations of contragradient lie algebras by
Vinay Deodhar(
Book
)
1 edition published in 1981 in English and held by 1 WorldCat member library worldwide
1 edition published in 1981 in English and held by 1 WorldCat member library worldwide
Cyclic elements in semisimple Lie algebras by A. G Elashvili(
)
1 edition published in 2012 in English and held by 1 WorldCat member library 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 1 WorldCat member library 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
Infinite dimensional groups with applications : talks given at the conference on infinite dimensional groups held at the Mathematical
Sciences Research Institute at Berkeley, California May 1015, 1984(
Book
)
1 edition published in 1985 in English and held by 1 WorldCat member library worldwide
1 edition published in 1985 in English and held by 1 WorldCat member library worldwide
Lie theory and geometry : in honor of Bertram Kostant by
J.L Brylinski(
Book
)
2 editions published in 1994 in English and held by 1 WorldCat member library 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 1 WorldCat member library 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
Quantum coadjoint action by C De Concini(
Book
)
2 editions published in 1991 in English and held by 1 WorldCat member library worldwide
2 editions published in 1991 in English and held by 1 WorldCat member library worldwide
Infinite dimensional lie algebras and groups : Conference : Papers(
Book
)
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras (2Nd Edition) by
Natasha Rozhkovskaya(
Book
)
1 edition published in 2013 in Undetermined and held by 1 WorldCat member library worldwide
1 edition published in 2013 in Undetermined and held by 1 WorldCat member library worldwide
Unendlichdimensionale LieAlgebren und Gruppen 21.4. bis 27.4.1985(
Book
)
1 edition published in 1985 in English and held by 1 WorldCat member library worldwide
1 edition published in 1985 in English and held by 1 WorldCat member library worldwide
Algebras, representations, and applications : a conference in honor of Ivan Shestakov's 60th birthday, August 26September
1, 2007, Maresias, Brazil by
V Futorny(
)
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
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Related Identities
 Raina, A. K. Contributor
 Rozhkovskaya, Natasha Author Contributor
 Cheung, Pokman Author
 Mathematical Sciences Research Institute (Berkeley, Calif.)
 Martinez, C. (Consuelo) 1955
 Zelmanov, Efim 1955
 Kashuba, Iryna
 Futorny, Vyacheslav Author
 Guillemin, Victor Editor
 De Concini, C. Author
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Associated Subjects
Algebra Algebras, Linear Calculus Combinatorial analysis Geometry Geometry, Algebraic Global analysis (Mathematics) Infinite dimensional Lie algebras Jordan algebras Lie algebras Lie groups Mathematical physics Mathematics Quantum field theory Quantum groups Quantum theory Superalgebras Topological groups Vertex operator algebras Von Neumann algebras
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.
Victor Kac mathématicien américain
Victor Kac Russisch wiskundige
Victor Kac SovietAmerican mathematician
Victor Kac USamerikanischer Mathematiker
Виктор Кац советский и американский математик
Віктор Кац
빅토르 카츠
ヴィクトル・カッツ
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