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Structure Of The Standard Modules For The Affine Lie Algebra A1 Superscript 1 Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Structure Of The Standard Modules For The Affine Lie Algebra A1 Superscript 1 book. This book definitely worth reading, it is an incredibly well-written.
Author : James Lepowsky
Publisher : Unknown
Page : 84 pages
File Size : 50,8 Mb
Release : 1985
Category : Lie algebras
ISBN : OCLC:15079910
Author : James Lepowsky,Mirko Primc
Publisher : American Mathematical Soc.
Page : 98 pages
File Size : 49,6 Mb
Release : 1985-12-31
Category : Mathematics
ISBN : 0821853961
The affine Kac-Moody algebra $A_1^{(1)}$ has recently served as a source of new ideas in the representation theory of infinite-dimensional affine Lie algebras. In particular, several years ago it was discovered that $A_1^{(1)}$ and then a general class of affine Lie algebras could be constructed using operators related to the vertex operators of the physicists' string model. This book develops the calculus of vertex operators to solve the problem of constructing all the standard $A_1^{(1)}$-modules in the homogeneous realization. Aimed primarily at researchers in and students of Lie theory, the book's detailed and concrete exposition makes it accessible and illuminating even to relative newcomers to the field.
Author : Marly Mandia
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 49,7 Mb
Release : 1987
Category : Mathematics
ISBN : 9780821824238
Author : John Brillhart
Publisher : American Mathematical Soc.
Page : 346 pages
File Size : 55,7 Mb
Release : 1988
Category : Mathematics
ISBN : 9780821850787
Author : James Lepowsky,Mirko Primc
Publisher : American Mathematical Soc.
Page : 84 pages
File Size : 40,6 Mb
Release : 1985
Category : Mathematics
ISBN : 9780821850480
The affine Kac-Moody algebra $A_1^{(1)}$ has recently served as a source of new ideas in the representation theory of infinite-dimensional affine Lie algebras. In particular, several years ago it was discovered that $A_1^{(1)}$ and then a general class of affine Lie algebras could be constructed using operators related to the vertex operators of the physicists' string model. This book develops the calculus of vertex operators to solve the problem of constructing all the standard $A_1^{(1)}$-modules in the homogeneous realization. Aimed primarily at researchers in and students of Lie theory, the book's detailed and concrete exposition makes it accessible and illuminating even to relative newcomers to the field.
Author : R.R. Bowker Company
Publisher : New York : R.R. Bowker
Page : 1390 pages
File Size : 45,7 Mb
Release : 1982
Category : Language Arts & Disciplines
ISBN : STANFORD:36105021374017
Author : Edward Frenkel
Publisher : Cambridge University Press
Page : 5 pages
File Size : 54,6 Mb
Release : 2007-06-28
Category : Mathematics
ISBN : 9780521854436
The first account of local geometric Langlands Correspondence, a new area of mathematical physics developed by the author.
Author : Victor G. Kac
Publisher : Springer Science & Business Media
Page : 267 pages
File Size : 52,8 Mb
Release : 2013-11-09
Category : Mathematics
ISBN : 9781475713824
Author : Alexander A. Kirillov
Publisher : Cambridge University Press
Page : 237 pages
File Size : 52,8 Mb
Release : 2008-07-31
Category : Mathematics
ISBN : 9780521889698
Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples
Author : Hermann Weyl
Publisher : Unknown
Page : 344 pages
File Size : 49,9 Mb
Release : 1946
Category : Mathematics
ISBN : STANFORD:36105002023716
In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from algebra, he examines the various properties of the groups. Analysis and topology are used wherever appropriate. The book also covers topics such as matrix algebras, semigroups, commutators, and spinors, which are of great importance in understanding the group-theoretic structure of quantum mechanics. Hermann Weyl was among the greatest mathematicians of the twentieth century. He made fundamental contributions to most branches of mathematics, but he is best remembered as one of the major developers of group theory, a powerful formal method for analyzing abstract and physical systems in which symmetry is present. In The Classical Groups, his most important book, Weyl provided a detailed introduction to the development of group theory, and he did it in a way that motivated and entertained his readers. Departing from most theoretical mathematics books of the time, he introduced historical events and people as well as theorems and proofs. One learned not only about the theory of invariants but also when and where they were originated, and by whom. He once said of his writing, "My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful." Weyl believed in the overall unity of mathematics and that it should be integrated into other fields. He had serious interest in modern physics, especially quantum mechanics, a field to which The Classical Groups has proved important, as it has to quantum chemistry and other fields. Among the five books Weyl published with Princeton, Algebraic Theory of Numbers inaugurated the Annals of Mathematics Studies book series, a crucial and enduring foundation of Princeton's mathematics list and the most distinguished book series in mathematics.
Author : Victor G. Kac
Publisher : American Mathematical Soc.
Page : 209 pages
File Size : 55,5 Mb
Release : 1998
Category : Mathematical physics
ISBN : 9780821813966
Based on courses given by the author at MIT and at Rome University in spring 1997, this book presents an introduction to algebraic aspects of conformal field theory. It includes material on the foundations of a rapidly growing area of algebraic conformal theory.
Author : Pavel Etingof,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik
Publisher : American Mathematical Soc.
Page : 344 pages
File Size : 41,9 Mb
Release : 2016-08-05
Category : Algebraic topology
ISBN : 9781470434410
Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
Author : Jean-Paul Dufour,Nguyen Tien Zung
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 44,5 Mb
Release : 2006-01-17
Category : Mathematics
ISBN : 9783764373351
The aim of this book is twofold. On the one hand, it gives a quick, self-contained introduction to Poisson geometry and related subjects. On the other hand, it presents a comprehensive treatment of the normal form problem in Poisson geometry. Even when it comes to classical results, the book gives new insights. It contains results obtained over the past 10 years which are not available in other books.
Author : Lynn Harold Loomis,Shlomo Sternberg
Publisher : World Scientific Publishing Company
Page : 596 pages
File Size : 47,6 Mb
Release : 2014-02-26
Category : Mathematics
ISBN : 9789814583954
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Author : P. K. Suetin,Alexandra I. Kostrikin,Yu I Manin
Publisher : CRC Press
Page : 324 pages
File Size : 47,8 Mb
Release : 1997-10-01
Category : Mathematics
ISBN : 9056990497
This advanced textbook on linear algebra and geometry covers a wide range of classical and modern topics. Differing from existing textbooks in approach, the work illustrates the many-sided applications and connections of linear algebra with functional analysis, quantum mechanics and algebraic and differential geometry. The subjects covered in some detail include normed linear spaces, functions of linear operators, the basic structures of quantum mechanics and an introduction to linear programming. Also discussed are Kahler's metic, the theory of Hilbert polynomials, and projective and affine geometries. Unusual in its extensive use of applications in physics to clarify each topic, this comprehensice volume should be of particular interest to advanced undergraduates and graduates in mathematics and physics, and to lecturers in linear and multilinear algebra, linear programming and quantum mechanics.
