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Author : Peter Goddard,David Olive
Publisher : World Scientific
Page : 610 pages
File Size : 45,9 Mb
Release : 1988
Category : Science
ISBN : 9971504200
This volume reviews the subject of Kac-Moody and Virasoro Algebras. It serves as a reference book for physicists with commentary notes and reprints.
Author : Neelacanta Sthanumoorthy,Kailash C. Misra
Publisher : American Mathematical Soc.
Page : 384 pages
File Size : 41,7 Mb
Release : 2004
Category : Kac-Moody algebras
ISBN : 9780821833377
This volume is the proceedings of the Ramanujan International Symposium on Kac-Moody Lie algebras and their applications. The symposium provided researchers in mathematics and physics with the opportunity to discuss new developments in this rapidly-growing area of research. The book contains several excellent articles with new and significant results. It is suitable for graduate students and researchers working in Kac-Moody Lie algebras, their applications, and related areas of research.
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 46,9 Mb
Release : 1988
Category : Electronic
ISBN : OCLC:916050824
Author : Victor G. Kac
Publisher : Cambridge University Press
Page : 428 pages
File Size : 48,7 Mb
Release : 1990
Category : Mathematics
ISBN : 0521466938
The third, substantially revised edition of a monograph concerned with Kac-Moody algebras, a particular class of infinite-dimensional Lie albegras, and their representations, based on courses given over a number of years at MIT and in Paris.
Author : Zhe-xian Wan
Publisher : World Scientific
Page : 172 pages
File Size : 46,5 Mb
Release : 1991-03-29
Category : Mathematics
ISBN : 9789814513906
This book is an introduction to a rapidly growing subject of modern mathematics, the Kac-Moody algebra, which was introduced by V Kac and R Moody simultanously and independently in 1968.
Author : E.A. de Kerf,G.G.A. Bäuerle,A.P.E. ten Kroode
Publisher : Elsevier
Page : 553 pages
File Size : 53,9 Mb
Release : 1997-10-30
Category : Science
ISBN : 0080535461
This is the long awaited follow-up to Lie Algebras, Part I which covered a major part of the theory of Kac-Moody algebras, stressing primarily their mathematical structure. Part II deals mainly with the representations and applications of Lie Algebras and contains many cross references to Part I. The theoretical part largely deals with the representation theory of Lie algebras with a triangular decomposition, of which Kac-Moody algebras and the Virasoro algebra are prime examples. After setting up the general framework of highest weight representations, the book continues to treat topics as the Casimir operator and the Weyl-Kac character formula, which are specific for Kac-Moody algebras. The applications have a wide range. First, the book contains an exposition on the role of finite-dimensional semisimple Lie algebras and their representations in the standard and grand unified models of elementary particle physics. A second application is in the realm of soliton equations and their infinite-dimensional symmetry groups and algebras. The book concludes with a chapter on conformal field theory and the importance of the Virasoro and Kac-Moody algebras therein.
Author : V G Kac
Publisher : World Scientific
Page : 640 pages
File Size : 46,6 Mb
Release : 1989-07-01
Category : Electronic
ISBN : 9789814663175
Contents:Integrable Representation of Kac-Moody Algebras: Results and Open Problems (V Chari & A Pressley)Existence of Certain Components in the Tensor Product of Two Integrable Highest Weight Modules for Kac-Moody Algebras (SKumar)Frobenius Action on the B-Cohomology (O Mathieu)Certain Rank Two Subsystems of Kac-Moody Root Systems (J Morita)Lie Groups Associated to Kac-Moody Lie Algebras: An Analytic Approach (E Rodriguez-Carrington)Almost Split-K-Forms of Kac-Moody Algebras (G Rousseau)Global Representations of the Diffeomorphism Groups of the Circle (F Bien)Path Space Realization of the Basic Representation of An(1) (E Date et al)Boson-Fermion Correspondence Over (C De Concini et al)Classification of Modular Invariant Representations of Affine Algebras (V G Kac & M Wakimoto)Standard Monomial Theory for SL2 (V Lakshmibai & C S Seshadri)Some Results on Modular Invariant Representations (S Lu)Current Algebras in 3+1 Space-Time Dimensions (J Mickelson)Standard Representations of An(1) (M Primc)Representations of the Algebra Uq(sI(2)), q-Orthogonal Polynomials and Invariants of Links (A N Kirillov & N Yu Reshetikhin)Infinite Super Grassmannians and Super Plücker Equations (M J Bergvelt)Drinfeld-Sokolov Hierarchies and t-Functions (H J Imbens)Super Boson-Fermion Correspondence of Type B (V G Kac & J W van de Leur)Prym Varieties and Soliton Equations (T Shiota)Polynomial Solutions of the BKP Hierarchy and Projective Representations of Symmetric Groups (Y You)Toward Generalized Macdonald's Identities (D Bernard)Conformal Theories with Non-Linearly Extended Virasoro Symmetries and Lie Algebra Classification (A Bilal & J-LGervais)Extended Conformal Algebras from Kac-Moody Algebras (P Bouwknegt)Meromorphic Conformal Field Theory (P Goddard)Local Extensions of the U(1) Current Algebra and Their Positive Energy Representations (R R Paunov & I T Todorov)Conformal Field Theory on Moduli Family of Stable Curves with Gauge Symmetries (A Tsuchiya & Y Yamada) Readership: Mathematicians and mathematical physicists
Author : Zhexian Wan
Publisher : World Scientific
Page : 178 pages
File Size : 52,7 Mb
Release : 1991
Category : Mathematics
ISBN : 9810202245
This book is an introduction to a rapidly growing subject of modern mathematics, the Kac-Moody algebra, which was introduced by V Kac and R Moody simultanously and independently in 1968.
Author : Robert V. Moody,Arturo Pianzola
Publisher : Wiley-Interscience
Page : 760 pages
File Size : 44,9 Mb
Release : 1995-04-17
Category : Mathematics
ISBN : UOM:39015034038276
Imparts a self-contained development of the algebraic theory of Kac-Moody algebras, their representations and close relatives--the Virasoro and Heisenberg algebras. Focuses on developing the theory of triangular decompositions and part of the Kac-Moody theory not specific to the affine case. Also covers lattices, and finite root systems, infinite-dimensional theory, Weyl groups and conjugacy theorems.
Author : Sam Kass,R. V. Moody,J. Patera,R. Slansky
Publisher : Univ of California Press
Page : 312 pages
File Size : 46,5 Mb
Release : 1990-01-01
Category : Science
ISBN : 0520067681
00 This practical treatise is an introduction to the mathematics and physics of affine Kac-Moody algebras. It is the result of an unusual interdisciplinary effort by two physicists and two mathematicians to make this field understandable to a broad readership and to illuminate the connections among seemingly disparate domains of mathematics and physics that are tantalizingly suggested by the ubiquity of Lie theory. The book will be useful to Lie algebraists, high energy physicists, statistical mechanics, and number theorists. Volume One contains a description of Kac-Moody Lie algebras, and especially the affine algebras and their representations; the results of extensive computations follow in Volume Two, which is spiral bound for easy reference. This practical treatise is an introduction to the mathematics and physics of affine Kac-Moody algebras. It is the result of an unusual interdisciplinary effort by two physicists and two mathematicians to make this field understandable to a broad readership and to illuminate the connections among seemingly disparate domains of mathematics and physics that are tantalizingly suggested by the ubiquity of Lie theory. The book will be useful to Lie algebraists, high energy physicists, statistical mechanics, and number theorists. Volume One contains a description of Kac-Moody Lie algebras, and especially the affine algebras and their representations; the results of extensive computations follow in Volume Two, which is spiral bound for easy reference.
Author : Michael David Weiner
Publisher : American Mathematical Soc.
Page : 121 pages
File Size : 43,7 Mb
Release : 1998
Category : Kac-Moody algebras
ISBN : 9780821808665
Begins with the bosonic construction of four level -1/2 irreducible representations of the symplectic affine Kac-Moody Lie algebra Cl. The direct sum of two of these is given the structure of a vertex operator algebra (VOA), and the direct sum of the other two is given the structure of a twisted VOA-module. The dissertation includes the bosonic analog of the fermionic construction of a vertex operator superalgebra from the four level 1 irreducible modules of type Dl. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Author : Minoru Wakimoto
Publisher : American Mathematical Soc.
Page : 332 pages
File Size : 55,7 Mb
Release : 2001
Category : Mathematics
ISBN : 0821826549
This volume begins with an introduction to the structure of finite-dimensional simple Lie algebras, including the representation of ...... root systems, the Cartan matrix, and a Dynkin diagram of a finite-dimensional simple Lie algebra. Continuing on, the main subjects of the book are the structure (real and imaginary root systems) of and the character formula for Kac-Moody superalgebras, which is explained in a very general setting. Only elementary linear algebra and group theory are assumed. Also covered is modular property and asymptotic behavior of integrable characters of affine Lie algebras. The exposition is self-contained and includes examples. The book can be used in a graduate-level course on the topic.
Author : Johnny T. Ottesen
Publisher : Springer Science & Business Media
Page : 223 pages
File Size : 41,9 Mb
Release : 2008-09-11
Category : Science
ISBN : 9783540491415
The idea of writing this book appeared when I was working on some problems related to representations of physically relevant infinite - mensional groups of operators on physically relevant Hilbert spaces. The considerations were local, reducing the subject to dealing with representations of infinite-dimensional Lie algebras associated with the associated groups. There is a large number of specialized articles and books on parts of this subject, but to our suprise only a few represent the point of view given in this book. Moreover, none of the written material was self-contained. At present, the subject has not reached its final form and active research is still being undertaken. I present this subject of growing importance in a unified manner and by a fairly simple approach. I present a route by which students can absorb and understand the subject, only assuming that the reader is familliar with functional analysis, especially bounded and unbounded operators on Hilbert spaces. Moreover, I assume a little basic knowledge of algebras , Lie algebras, Lie groups, and manifolds- at least the definitions. The contents are presented in detail in the introduction in Chap. The manuscript of this book has been succesfully used by some advanced graduate students at Aarhus University, Denmark, in their "A-exame'. I thank them for comments.
Author : Jouko Mickelsson
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 45,9 Mb
Release : 2013-03-09
Category : Science
ISBN : 9781475702958
Let M be a smooth manifold and G a Lie group. In this book we shall study infinite-dimensional Lie algebras associated both to the group Map(M, G) of smooth mappings from M to G and to the group of dif feomorphisms of M. In the former case the Lie algebra of the group is the algebra Mg of smooth mappings from M to the Lie algebra gof G. In the latter case the Lie algebra is the algebra Vect M of smooth vector fields on M. However, it turns out that in many applications to field theory and statistical physics one must deal with certain extensions of the above mentioned Lie algebras. In the simplest case M is the unit circle SI, G is a simple finite dimensional Lie group and the central extension of Map( SI, g) is an affine Kac-Moody algebra. The highest weight theory of finite dimensional Lie algebras can be extended to the case of an affine Lie algebra. The important point is that Map(Sl, g) can be split to positive and negative Fourier modes and the finite-dimensional piece g corre sponding to the zero mode.
Author : Victor G Kac,Ashok K Raina,Natasha Rozhkovskaya
Publisher : World Scientific
Page : 252 pages
File Size : 42,6 Mb
Release : 2013-07-05
Category : Science
ISBN : 9789814522212
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∞ 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 Kac–Moody) 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 lambda-bracket, energy-momentum 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 two-dimensional statistical models, and string theory. Contents:Definition of Positive-Energy Representations of VirComplete Reducibility of the Oscillator Representations of VirLie Algebras of Infinite MatricesBoson–Fermion CorrespondenceSchur PolynomialsN-Soliton SolutionsThe Kac Determinant FormulaNonabelian Generalization of Virasoro Operators: The Sugawara ConstructionThe Weyl–Kac Character Formula and Jacobi–Riemann Theta FunctionsCompletion of the Proof of the Kac Determinant FormulaLambda–Bracket of Local Formal DistributionsCompletion of U, Restricted Representations and Quantum FieldsNon-Commutative Wick FormulaConformal WeightsDefinition of a Vertex AlgebraDefinition of a Representation of a Vertex Algebraand other lectures Readership: Mathematicians studying representation theory and theoretical physicists. Keywords:Highest Weight Representations;Virasoro Algebra;Heisenberg Algebra;Infinite-Dimensional Lie Algebras;BosonâFermion Correspondence;Sugawara Construction;Kac Determinant Formula;Vertex Operators;The KP Hierarchy;N-Solitons;Hirota's Bilinear Equations;Vertex Algebras;Quantum Fields;Energy-Momentum Field;Lambda-Bracket;Normal Ordered Product;Conformal Weight;Twisted Representations;Zhu Algebra;Charged Free Fermions;Neutral Free Fermions;Borcherds Identity;Twisted RepresentationsKey Features:The first part of the lectures demonstrates four related constructions of highest weight representations of infinite-dimensional algebras: Heisenberg algebra, Lie algebra $gl_\infty$, affine Kac–Moody algebras and the Virasoro algebra. The constructions originate from theoretical physics and are explained in full detailThe complete proof of the Kac determinant formula is providedThe second part of the lectures demonstrates how the notions of the theory of vertex algebras clarify and simplify the constructions of the first partThe introductory exposition is self-containedMany examples providedCan be used for graduate courses