Kac, Victor G. 1943
Overview
Works:  33 works in 183 publications in 4 languages and 4,132 library holdings 

Genres:  Conference proceedings 
Roles:  Author, Editor 
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(
)
25 editions published between 1987 and 2013 in English and held by 1,467 WorldCat member libraries worldwide
The first edition of this book is a collection of a series of lectures given by Professor Victor Kac at the TIFR, Mumbai, India in December 1985 and January 1986. 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 infinite dimensional 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, Kas
25 editions published between 1987 and 2013 in English and held by 1,467 WorldCat member libraries worldwide
The first edition of this book is a collection of a series of lectures given by Professor Victor Kac at the TIFR, Mumbai, India in December 1985 and January 1986. 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 infinite dimensional 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, Kas
Infinite dimensional Lie algebras
by
Victor G Kac(
Book
)
54 editions published between 1982 and 2006 in 4 languages and held by 1,016 WorldCat member libraries worldwide
54 editions published between 1982 and 2006 in 4 languages and held by 1,016 WorldCat member libraries worldwide
Vertex algebras for beginners
by
Victor G Kac(
Book
)
25 editions published between 1996 and 2001 in English and held by 504 WorldCat member libraries worldwide
25 editions published between 1996 and 2001 in English and held by 504 WorldCat member libraries worldwide
Quantum calculus
by
Victor G Kac(
Book
)
12 editions published between 2001 and 2002 in English and held by 369 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
12 editions published between 2001 and 2002 in English and held by 369 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
)
11 editions published in 1985 in English and held by 328 WorldCat member libraries worldwide
11 editions published in 1985 in English and held by 328 WorldCat member libraries worldwide
Graded simple Jordan superalgebras of growth one
by
Victor G Kac(
Book
)
11 editions published in 2001 in English and held by 234 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 234 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
(
Book
)
11 editions published in 1989 in English and held by 155 WorldCat member libraries worldwide
11 editions published in 1989 in English and held by 155 WorldCat member libraries worldwide
Lie theory and geometry : in honor of Bertram Kostant
by
J.L Brylinski(
)
3 editions published in 1994 in English and held by 21 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
3 editions published in 1994 in English and held by 21 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
Highest Weight Representations of Infinite Dimensional Lie Algebra
by
Victor G Kac(
)
2 editions published in 1988 in English and held by 11 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
2 editions published in 1988 in English and held by 11 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
Infinite dimensional lie algebras and groups : Proceedings of the conference held at CIRM, Luminy, Marseille
by
Victor G Kac(
Book
)
2 editions published in 1989 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1989 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
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
Characters and fusion rules for Walgebras via quantized DrinfeldSokolov reductions
by
Edward Frenkel(
Book
)
1 edition 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."
1 edition 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."
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
Infinite dimensional lie algebras and groups : Conference : Papers
(
)
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
Trace formula for graded lie algebras and monstrous moonshine
by
Victor G Kac(
Book
)
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
A new class of unitarizable highest weight representations of infinite dimensional Lie algebras
by
Hans Plesner Jakobsen(
Book
)
1 edition published in 1987 in Danish and held by 1 WorldCat member library worldwide
1 edition published in 1987 in Danish 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
Representations of quantum groups at roots of 1
by C De Concini(
Book
)
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
1 edition published in 1990 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
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Related Identities
 Raina, A. K. Contributor
 Rozhkovskaya, Natasha Contributor
 Cheung, Pokman Author
 Mathematical Sciences Research Institute (Berkeley, Calif.)
 Zelmanov, Efim 1955
 Martinez, C. (Consuelo) 1955
 Brylinski, Ranee Editor
 Brylinski, J.L (JeanLuc) Author Editor
 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) Group theory 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