Kac, Victor G. 1943
Overview
Works:  33 works in 216 publications in 5 languages and 4,856 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
)
65 editions published between 1982 and 2014 in 5 languages and held by 1,029 WorldCat member libraries worldwide
This is the third, substantially revised edition of this important monograph. The book is concerned with Kac–Moody algebras, a particular class of infinitedimensional Lie algebras, and their representations. It is based on courses given over a number of years at MIT and in Paris, and is sufficiently selfcontained and detailed to be used for graduate courses. Each chapter begins with a motivating discussion and ends with a collection of exercises, with hints to the more challenging problems
65 editions published between 1982 and 2014 in 5 languages and held by 1,029 WorldCat member libraries worldwide
This is the third, substantially revised edition of this important monograph. The book is concerned with Kac–Moody algebras, a particular class of infinitedimensional Lie algebras, and their representations. It is based on courses given over a number of years at MIT and in Paris, and is sufficiently selfcontained and detailed to be used for graduate courses. Each chapter begins with a motivating discussion and ends with a collection of exercises, with hints to the more challenging problems
Vertex algebras for beginners by
Victor G Kac(
Book
)
24 editions published between 1996 and 2001 in English and held by 513 WorldCat member libraries worldwide
24 editions published between 1996 and 2001 in English and held by 513 WorldCat member libraries worldwide
Quantum calculus by
Victor G Kac(
Book
)
18 editions published between 2001 and 2011 in English and held by 363 WorldCat member libraries worldwide
Introduction <br>• qderivative and hderivative <br>• Generalized Taylor’s formula for polynomials <br>• qanalogue of (xa)subn, n an integer, and qderivatives of binomials <br>• qTaylor’s formula for polynomials <br>• Gauss’ binomial formula and a noncommutative binomial formula <br>• Properties of qbinomial coefficients <br>• qbinomial coefficients and linear algebra over finite fields <br>• qTaylor’s formula for formal power series and Heine’s binomial formula <br>• Two Euler identities and two qexponential functions <br>• qtrigonometric functions <br>• Jacobi’s triple product identity <br>• Classical partition function and Euler’s product formula <br>• qhypergeometric functions and Heine’s formula <br>• More on Heine’s formula and the general binomial <br>• Ramanujan’s product formula <br>• Explicit formulas for sums of two and of four squares <br>• Explicit formulas for sums of two and of four triangular numbers <br>• qantiderivative <br>• Jackson integral <br>• Fundamental theorem of qcalculus and integration by parts <br>• qgamma and qbeta functions <br>• hderivative and hintegral <br>• Bernoulli polynomials and Bernoulli numbers <br>• Sums of powers <br>• EulerMaclaurin formula <br>• Symmetric quantum calculus <br>• Appendix: a list of qantiderivatives <br>• Literature<br>
18 editions published between 2001 and 2011 in English and held by 363 WorldCat member libraries worldwide
Introduction <br>• qderivative and hderivative <br>• Generalized Taylor’s formula for polynomials <br>• qanalogue of (xa)subn, n an integer, and qderivatives of binomials <br>• qTaylor’s formula for polynomials <br>• Gauss’ binomial formula and a noncommutative binomial formula <br>• Properties of qbinomial coefficients <br>• qbinomial coefficients and linear algebra over finite fields <br>• qTaylor’s formula for formal power series and Heine’s binomial formula <br>• Two Euler identities and two qexponential functions <br>• qtrigonometric functions <br>• Jacobi’s triple product identity <br>• Classical partition function and Euler’s product formula <br>• qhypergeometric functions and Heine’s formula <br>• More on Heine’s formula and the general binomial <br>• Ramanujan’s product formula <br>• Explicit formulas for sums of two and of four squares <br>• Explicit formulas for sums of two and of four triangular numbers <br>• qantiderivative <br>• Jackson integral <br>• Fundamental theorem of qcalculus and integration by parts <br>• qgamma and qbeta functions <br>• hderivative and hintegral <br>• Bernoulli polynomials and Bernoulli numbers <br>• Sums of powers <br>• EulerMaclaurin formula <br>• Symmetric quantum calculus <br>• Appendix: a list of qantiderivatives <br>• Literature<br>
Infinite dimensional groups with applications by
Victor G Kac(
Book
)
15 editions published in 1985 in English and held by 351 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
15 editions published in 1985 in English and held by 351 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
)
13 editions published between 1987 and 2012 in English and held by 260 WorldCat member libraries worldwide
This book is a collection of a series of lectures given by Prof. V Kac at Tata Institute, India in Dec '85 and Jan '86. These lectures focus on the idea of a highest weight representation, which goes through four different incarnations. The first is the canonical commutation relations of the infinitedimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra gl 8 of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary hi
13 editions published between 1987 and 2012 in English and held by 260 WorldCat member libraries worldwide
This book is a collection of a series of lectures given by Prof. V Kac at Tata Institute, India in Dec '85 and Jan '86. These lectures focus on the idea of a highest weight representation, which goes through four different incarnations. The first is the canonical commutation relations of the infinitedimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra gl 8 of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary hi
Graded simple Jordan superalgebras of growth one by
Victor G Kac(
Book
)
12 editions published in 2001 in English and held by 227 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
12 editions published in 2001 in English and held by 227 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
)
17 editions published between 1989 and 1990 in English and held by 169 WorldCat member libraries worldwide
"Readership: Mathematicians and mathematical physicists."
17 editions published between 1989 and 1990 in English and held by 169 WorldCat member libraries worldwide
"Readership: Mathematicians and mathematical physicists."
Bombay lectures on highest weight representations of infinite dimensional lie algebras by
Victor G Kac(
Book
)
15 editions published between 1987 and 2013 in English and held by 69 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
15 editions published between 1987 and 2013 in English and held by 69 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
Representations of quantum groups at roots of 1 : reduction to the exceptional case by
Corrado De Concini(
Book
)
4 editions published between 1990 and 1991 in English and held by 3 WorldCat member libraries worldwide
4 editions published between 1990 and 1991 in English and held by 3 WorldCat member libraries worldwide
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
A new class of unitarizable highest weight representations of infinite dimensional Lie algebras by
Hans Plesner Jakobsen(
Book
)
2 editions published in 1987 in Danish and English and held by 2 WorldCat member libraries worldwide
2 editions published in 1987 in Danish and English and held by 2 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 2 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 2 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."
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
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
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
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
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
Vertex algebras for beginners : Victor Kac by
Victor G Kac(
)
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
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
Highest Weight Representations of Infinite Dimensional Lie Algebra by
Victor G Kac(
Book
)
2 editions published in 1988 in English and held by 1 WorldCat member library worldwide
This book is a collection of a series of lectures given by Prof. V Kac at Tata Institute, India in Dec '85 and Jan '86. These lectures focus on the idea of a highest weight representation, which goes through four different incarnations. The first is the canonical commutation relations of the infinitedimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra gl 8 of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary hi
2 editions published in 1988 in English and held by 1 WorldCat member library worldwide
This book is a collection of a series of lectures given by Prof. V Kac at Tata Institute, India in Dec '85 and Jan '86. These lectures focus on the idea of a highest weight representation, which goes through four different incarnations. The first is the canonical commutation relations of the infinitedimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra gl 8 of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary hi
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Related Identities
 Raina, A. K. Contributor
 Rozhkovskaya, Natasha Author Contributor
 Cheung, Pokman Author
 Mathematical Sciences Research Institute (Berkeley, Calif.)
 Zelmanov, Efim 1955
 Martinez, C. (Consuelo) 1955
 De Concini, C. Author
 De Concini, C. Author
 Procesi, C.
 Elashvili, A. G. Author
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Associated Subjects
Algebras, Linear Calculus Combinatorial analysis Global analysis (Mathematics) Global differential geometry Infinite dimensional Lie algebras Jordan algebras Lie algebras Lie groups Mathematical physics Mathematics Number theory Quantum field theory Quantum groups Quantum theory Superalgebras Topological groups Topology 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 matemático ruso
Victor Kac mathématicien américain
Victor Kac Russisch wiskundige
Victor Kac SovietAmerican mathematician
Victor Kac USamerikanischer Mathematiker
Віктор Кац
Кац, Виктор советский и американский математик
빅토르 카츠
ヴィクトル・カッツ
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