Kac, Victor G. 1943Overview
Most widely held works by
Victor G Kac
Infinite dimensional Lie algebras
by Victor G Kac
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Book
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51 editions published between 1982 and 2006 in English and Undetermined and held by 991 WorldCat member libraries worldwide
Vertex algebras for beginners
by Victor G Kac
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Book
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22 editions published between 1996 and 2001 in English and held by 497 WorldCat member libraries worldwide
Quantum calculus
by Victor G Kac
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Book
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11 editions published between 2001 and 2002 in English and held by 347 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
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Book
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14 editions published in 1985 in English and held by 338 WorldCat member libraries worldwide
Bombay lectures on highest weight representations of infinite dimensional lie algebras
by Victor G Kac
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Book
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17 editions published between 1987 and 2013 in English and held by 331 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[symbol] 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 highest weight representations of the current (= affine KacMoody) algebras. These Lie algebras appear in the lectures in connection to the Sugawara construction, which is the main tool in the study of the fourth incarnation of the main idea, the theory of the highest weight representations of the Virasoro algebra. In particular, the book provides a complete proof of the Kac determinant formula, the key result in representation theory of the Virasoro algebra. 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 algebras  such as quantum fields, their normal ordered product and lambdabracket, energymomentum field and conformal weight, untwisted and twisted representations  simplify and clarify the constructions of the first edition of the book. This book should be very useful for both mathematicians and physicists. 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
Graded simple Jordan superalgebras of growth one
by Victor G Kac
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Book
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10 editions published in 2001 in English and held by 223 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
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Book
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9 editions published in 1989 in English and held by 154 WorldCat member libraries worldwide
Highest Weight Representations of Infinite Dimensional Lie Algebra
by Victor G Kac
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2 editions published in 1988 in English and held by 8 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
Beskonechnomernye algebry Li
by Victor G Kac
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Book
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2 editions published in 1993 in Russian and held by 3 WorldCat member libraries worldwide
Lie theory and geometry : in honor of Bertram Kostant
by J.L Brylinski
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2 editions published in 1994 in English and held by 3 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
Quasifinite representations of classical Lie subalgebras of W1+∞
by Victor G Kac
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2 editions published in 1998 in English and held by 2 WorldCat member libraries worldwide
Characters and fusion rules for Walgebras via quantized DrinfeldSokolov reductions
by Edward Frenkel
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Book
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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."
Ėkonomičeskoe sorevnovanie meždu S[ojuzom] SSR i SŠA
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Book
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1 edition published in 1959 in Undetermined and held by 2 WorldCat member libraries worldwide
Torsion in cohomology of compact Lie groups
by Victor G Kac
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Book
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1 edition published in 1984 in English and held by 2 WorldCat member libraries worldwide
Trace formula for graded lie algebras and monstrous moonshine
by Victor G Kac
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Book
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1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
Advanced series in mathematical physics
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in English and held by 1 WorldCat member library worldwide
Unendlichdimensionale LieAlgebren und Gruppen 21.4. bis 27.4.1985
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Book
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1 edition published in 1985 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
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Book
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1 edition published in 1987 in Danish and held by 1 WorldCat member library worldwide
BOMBAY LECTURES ON HIGHEST WEIGHT REPRESENTATIONS OF INFINITE DIMENSIONAL LIE ALGEBRAS (2ND EDITION)
by Victor G Kac
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1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
Unendlichdimensionale einfache LieAlgebren 29.6. bis 5.7.1980
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Book
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1 edition published in 1980 in English and held by 1 WorldCat member library worldwide more
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Related Identities
Associated Subjects
Algebras, Linear Calculus Combinatorial analysis Geometry Global analysis (Mathematics) Group theory Infinite dimensional Lie algebras Jordan algebras Lie algebras Lie groups Mathematical physics Mathematics Quantum field theory Quantum theory Superalgebras 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.
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