Introduction To Kac Moody Algebras

Introduction To Kac moody Algebras PDF
Author: Zhe-xian Wan
Publisher: World Scientific
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 172
View: 1852
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Book Description: 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.


Introduction To Kac Moody Algebra

Introduction to Kac Moody Algebra PDF
Author: Zhexian Wan
Publisher: World Scientific
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 178
View: 4027
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Book Description: 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.


Introduction To Kac Moody Algebras

Introduction to Kac Moody Algebras PDF
Author: Wan Zhe-xian
Publisher:
Format: PDF, ePub, Mobi
Category : Kac-Moody algebras
Languages : en
Pages :
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Book Description:


An Introduction To Kac Moody Groups Over Fields

An Introduction to Kac   Moody Groups Over Fields PDF
Author: Timothée Marquis
Publisher:
Format: PDF, ePub, Mobi
Category : MATHEMATICS
Languages : en
Pages : 331
View: 4590
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Book Description: The interest for Kac–Moody algebras and groups has grown exponentially in the past decades, both in the mathematical and physics communities, and with it also the need for an introductory textbook on the topic. The aims of this book are twofold: - to offer an accessible, reader-friendly and self-contained introduction to Kac–Moody algebras and groups; - to clean the foundations and to provide a unified treatment of the theory. The book starts with an outline of the classical Lie theory, used to set the scene. Part II provides a self-contained introduction to Kac–Moody algebras. The heart of the book is Part III, which develops an intuitive approach to the construction and fundamental properties of Kac–Moody groups. It is complemented by two appendices, respectively offering introductions to affine group schemes and to the theory of buildings. Many exercises are included, accompanying the readers throughout their journey. The book assumes only a minimal background in linear algebra and basic topology, and is addressed to anyone interested in learning about Kac–Moody algebras and/or groups, from graduate (master) students to specialists.


Infinite Dimensional Lie Algebras

Infinite Dimensional Lie Algebras PDF
Author: Victor G. Kac
Publisher: Springer Science & Business Media
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 267
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Affine Lie Algebras Weight Multiplicities And Branching Rules

Affine Lie Algebras  Weight Multiplicities  and Branching Rules PDF
Author: Sam Kass
Publisher: Univ of California Press
Format: PDF, ePub, Mobi
Category : Science
Languages : en
Pages : 312
View: 6882
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Book Description: 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.


Kac Moody Groups Their Flag Varieties And Representation Theory

Kac Moody Groups  their Flag Varieties and Representation Theory PDF
Author: Shrawan Kumar
Publisher: Springer Science & Business Media
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 613
View: 6473
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Book Description: Kac-Moody Lie algebras 9 were introduced in the mid-1960s independently by V. Kac and R. Moody, generalizing the finite-dimensional semisimple Lie alge bras which we refer to as the finite case. The theory has undergone tremendous developments in various directions and connections with diverse areas abound, including mathematical physics, so much so that this theory has become a stan dard tool in mathematics. A detailed treatment of the Lie algebra aspect of the theory can be found in V. Kac's book [Kac-90l This self-contained work treats the algebro-geometric and the topological aspects of Kac-Moody theory from scratch. The emphasis is on the study of the Kac-Moody groups 9 and their flag varieties XY, including their detailed construction, and their applications to the representation theory of g. In the finite case, 9 is nothing but a semisimple Y simply-connected algebraic group and X is the flag variety 9 /Py for a parabolic subgroup p y C g.


Lie Algebras Of Finite And Affine Type

Lie Algebras of Finite and Affine Type PDF
Author: Roger William Carter
Publisher: Cambridge University Press
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 662
View: 2898
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Book Description: This book provides a thorough but relaxed mathematical treatment of Lie algebras.


Introduction To Finite And Infinite Dimensional Lie Super Algebras

Introduction to Finite and Infinite Dimensional Lie  Super algebras PDF
Author: Neelacanta Sthanumoorthy
Publisher: Academic Press
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 512
View: 6832
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Book Description: Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras. Discusses the fundamental structure and all root relationships of Lie algebras and Lie superalgebras and their finite and infinite dimensional representation theory Closely describes BKM Lie superalgebras, their different classes of imaginary root systems, their complete classifications, root-supermultiplicities, and related combinatorial identities Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras Focuses on Kac-Moody algebras


Introduction To Lie Algebras And Representation Theory

Introduction to Lie Algebras and Representation Theory PDF
Author: J.E. Humphreys
Publisher: Springer Science & Business Media
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 189
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Book Description: This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are admittedly a little more demanding. Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements have been made even in the classical parts of the theory. I have tried to incor porate some of them here and to provide easier access to the subject for non-specialists. For the specialist, the following features should be noted: (I) The Jordan-Chevalley decomposition of linear transformations is emphasized, with "toral" subalgebras replacing the more traditional Cartan subalgebras in the semisimple case. (2) The conjugacy theorem for Cartan subalgebras is proved (following D. J. Winter and G. D. Mostow) by elementary Lie algebra methods, avoiding the use of algebraic geometry.


Some Generalized Kac Moody Algebras With Known Root Multiplicities

Some Generalized Kac Moody Algebras with Known Root Multiplicities PDF
Author: Nanhua XI
Publisher:
Format: PDF, Kindle
Category : Electronic books
Languages : en
Pages : 119
View: 175
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Book Description: Introduction Generalized Kac-Moody algebras Modular forms Lattices and their Theta-functions The proof of Theorem 1.7 The real simple roots Hyperbolic Lie algebras Appendix A Appendix B Bibliography Notation


Kac Moody And Virasoro Algebras

Kac Moody and Virasoro Algebras PDF
Author: Peter Goddard
Publisher: World Scientific
Format: PDF, ePub, Docs
Category : Science
Languages : en
Pages : 610
View: 3264
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Book Description: This volume reviews the subject of Kac-Moody and Virasoro Algebras. It serves as a reference book for physicists with commentary notes and reprints.


Infinite Dimensional Lie Algebras

Infinite dimensional Lie Algebras PDF
Author: Minoru Wakimoto
Publisher: American Mathematical Soc.
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 332
View: 5768
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Book Description: 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.


Introduction To Lie Algebras

Introduction to Lie Algebras PDF
Author: K. Erdmann
Publisher: Springer Science & Business Media
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 251
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Book Description: Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right. This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates. The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality. Numerous worked examples and exercises are provided to test understanding, along with more demanding problems, several of which have solutions. Introduction to Lie Algebras covers the core material required for almost all other work in Lie theory and provides a self-study guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics.


Langlands Correspondence For Loop Groups

Langlands Correspondence for Loop Groups PDF
Author: Edward Frenkel
Publisher: Cambridge University Press
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 5
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Book Description: The first account of local geometric Langlands Correspondence, a new area of mathematical physics developed by the author.


Vertex Algebras And Algebraic Curves

Vertex Algebras and Algebraic Curves PDF
Author: Edward Frenkel
Publisher: American Mathematical Soc.
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 418
View: 2924
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Book Description: Vertex algebras are algebraic objects that encapsulate the concept of operator product expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming ubiquitous in many areas of modern mathematics, with applications to representation theory, algebraic geometry, the theory of finite groups, modular functions, topology, integrable systems, and combinatorics. This book is an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. The notion of a vertex algebra is introduced in a coordinate-independent way, so that vertex operators become well defined on arbitrary smooth algebraic curves, possibly equipped with additional data, such as a vector bundle. Vertex algebras then appear as the algebraic objects encoding the geometric structure of various moduli spaces associated with algebraic curves. Therefore they may be used to give a geometric interpretation of various questions of representation theory. The book contains many original results, introduces important new concepts, and brings new insights into the theory of vertex algebras. The authors have made a great effort to make the book self-contained and accessible to readers of all backgrounds. Reviewers of the first edition anticipated that it would have a long-lasting influence on this exciting field of mathematics and would be very useful for graduate students and researchers interested in the subject. This second edition, substantially improved and expanded, includes several new topics, in particular an introduction to the Beilinson-Drinfeld theory of factorization algebras and the geometric Langlands correspondence.


Introduction To Quantum Groups

Introduction to Quantum Groups PDF
Author: George Lusztig
Publisher: Springer Science & Business Media
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 352
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Book Description: The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties. This book will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists and to theoretical physicists and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the book could also be used as a text book.


Lie Algebras With Triangular Decompositions

Lie Algebras with Triangular Decompositions PDF
Author: Robert V. Moody
Publisher: Wiley-Interscience
Format: PDF
Category : Mathematics
Languages : en
Pages : 760
View: 6367
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Book Description: 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.


Group Theory In Physics

Group Theory in Physics PDF
Author: John F. Cornwell
Publisher: Academic Press
Format: PDF, ePub, Docs
Category : Science
Languages : en
Pages : 361
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Book Description: This book, an abridgment of Volumes I and II of the highly respected Group Theory in Physics, presents a carefully constructed introduction to group theory and its applications in physics. The book provides anintroduction to and description of the most important basic ideas and the role that they play in physical problems. The clearly written text contains many pertinent examples that illustrate the topics, even for those with no background in group theory.This work presents important mathematical developments to theoretical physicists in a form that is easy to comprehend and appreciate. Finite groups, Lie groups, Lie algebras, semi-simple Lie algebras, crystallographic point groups and crystallographic space groups, electronic energy bands in solids, atomic physics, symmetry schemes for fundamental particles, and quantum mechanics are all covered in this compact new edition. Covers both group theory and the theory of Lie algebras Includes studies of solid state physics, atomic physics, and fundamental particle physics Contains a comprehensive index Provides extensive examples


Quantum Lie Theory

Quantum Lie Theory PDF
Author: Vladislav Kharchenko
Publisher: Springer
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 302
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Book Description: This is an introduction to the mathematics behind the phrase “quantum Lie algebra”. The numerous attempts over the last 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary “quantum” Lie bracket have not been widely accepted. In this book, an alternative approach is developed that includes multivariable operations. Among the problems discussed are the following: a PBW-type theorem; quantum deformations of Kac--Moody algebras; generic and symmetric quantum Lie operations; the Nichols algebras; the Gurevich--Manin Lie algebras; and Shestakov--Umirbaev operations for the Lie theory of nonassociative products. Opening with an introduction for beginners and continuing as a textbook for graduate students in physics and mathematics, the book can also be used as a reference by more advanced readers. With the exception of the introductory chapter, the content of this monograph has not previously appeared in book form.