Kac-Moody and Virasoro Algebras PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Kac-Moody and Virasoro Algebras PDF full book. Access full book title Kac-Moody and Virasoro Algebras by Peter Goddard. Download full books in PDF and EPUB format.
Author: Peter Goddard
Publisher: World Scientific
ISBN: 9789971504205
Category : Science
Languages : en
Pages : 610
Get Book Here
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.
Author: Peter Goddard
Publisher: World Scientific
ISBN: 9789971504205
Category : Science
Languages : en
Pages : 610
Get Book Here
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.
Author: J. Lepowsky
Publisher: Springer Science & Business Media
ISBN: 146139550X
Category : Science
Languages : en
Pages : 484
Get Book Here
Book Description
James Lepowsky t The search for symmetry in nature has for a long time provided representation theory with perhaps its chief motivation. According to the standard approach of Lie theory, one looks for infinitesimal symmetry -- Lie algebras of operators or concrete realizations of abstract Lie algebras. A central theme in this volume is the construction of affine Lie algebras using formal differential operators called vertex operators, which originally appeared in the dual-string theory. Since the precise description of vertex operators, in both mathematical and physical settings, requires a fair amount of notation, we do not attempt it in this introduction. Instead we refer the reader to the papers of Mandelstam, Goddard-Olive, Lepowsky-Wilson and Frenkel-Lepowsky-Meurman. We have tried to maintain consistency of terminology and to some extent notation in the articles herein. To help the reader we shall review some of the terminology. We also thought it might be useful to supplement an earlier fairly detailed exposition of ours [37] with a brief historical account of vertex operators in mathematics and their connection with affine algebras. Since we were involved in the development of the subject, the reader should be advised that what follows reflects our own understanding. For another view, see [29].1 t Partially supported by the National Science Foundation through the Mathematical Sciences Research Institute and NSF Grant MCS 83-01664. 1 We would like to thank Igor Frenkel for his valuable comments on the first draft of this introduction.
Author: C Itzykson
Publisher: World Scientific
ISBN: 9814507598
Category :
Languages : en
Pages : 992
Get Book Here
Book Description
This volume contains Introductory Notes and major reprints on conformal field theory and its applications to 2-dimensional statistical mechanics of critical phenomena. The subject relates to many different areas in contemporary physics and mathematics, including string theory, integrable systems, representations of infinite Lie algebras and automorphic functions.
Author: Robert V. Moody
Publisher: Wiley-Interscience
ISBN:
Category : Mathematics
Languages : en
Pages : 760
Get Book Here
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.
Author: John F. Cornwell
Publisher: Academic Press
ISBN: 0080532667
Category : Science
Languages : en
Pages : 361
Get Book Here
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
Author: Edward Frenkel
Publisher: American Mathematical Soc.
ISBN: 0821836749
Category : Mathematics
Languages : en
Pages : 418
Get Book Here
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.
Author: Lars Brink
Publisher: World Scientific
ISBN: 9789971509804
Category : Science
Languages : en
Pages : 616
Get Book Here
Book Description
Vadim Knizhnik was one of the most promising theoretical physicists in the world. Unfortunately, he passed away at the very young age of 25 years. This memorial volume is to honor his contributions in Theoretical Physics. This is perhaps one of the most important collections of articles on the theoretical developments in String Theory, Conformal Field Theory and related topics. It consists of contributions from world-renowned physicists who have met Vadim Knizhnik personally and whom the late Knizhnik really respected. The contributions are systematic and pedagogical in format.
Author: Roger William Carter
Publisher: Cambridge University Press
ISBN: 9780521851381
Category : Mathematics
Languages : en
Pages : 662
Get Book Here
Book Description
This book provides a thorough but relaxed mathematical treatment of Lie algebras.
Author: J.E. Humphreys
Publisher: Springer Science & Business Media
ISBN: 1461263980
Category : Mathematics
Languages : en
Pages : 189
Get Book Here
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.
Author: Sergio Albeverio
Publisher: Cambridge University Press
ISBN: 9780521556101
Category : Mathematics
Languages : en
Pages : 148
Get Book Here
Book Description
This book deals with the mathematical aspects of string theory.
