Representations of Infinite Dimensional Lie Algebras and Lie Groups on Fock Space
Author: Ole Rask Jensen
Publisher:
Published: 1996
Total Pages: 44
ISBN-13:
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Author: Ole Rask Jensen
Publisher:
Published: 1996
Total Pages: 44
ISBN-13:
DOWNLOAD EBOOKAuthor: Erik Bjerrum Nielsen
Publisher:
Published: 1996
Total Pages: 44
ISBN-13:
DOWNLOAD EBOOKAuthor: Anatoliĭ Moiseevich Vershik
Publisher: CRC Press
Published: 1990
Total Pages: 576
ISBN-13: 9782881246784
DOWNLOAD EBOOKEight papers provide mature readers with careful review of progress (through about 1983) toward the creation of a theory of the representations of infinite-dimensional Lie groups and algebras, and of some related topics. Recent developments in physics have provided major impetus for the development of such a theory, and the volume will be of special interest to mathematical physicists (quantum field theorists). Translated from the Russian edition of unstated date, and beautifully produced (which--at the price--it should be!). Book club price, $118. (NW) Annotation copyrighted by Book News, Inc., Portland, OR
Author: Johnny T. Ottesen
Publisher: Springer Science & Business Media
Published: 2008-09-11
Total Pages: 223
ISBN-13: 3540491414
DOWNLOAD EBOOKThe 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: Jean Marion
Publisher: World Scientific
Published: 1998-10-30
Total Pages: 410
ISBN-13: 9814544841
DOWNLOAD EBOOKThis proceedings volume can be considered as a monograph on the state-of-the-art in the wide range of analysis on infinite-dimensional algebraic-topological structures. Topics covered in this volume include integrability and regularity for Lie groups and Lie algebras, actions of infinite-dimensional Lie groups on manifolds of paths and related minimal orbits, quasi-invariant measures, white noise analysis, harmonic analysis on generalized convolution structures, and noncommutative geometry. A special feature of this volume is the interrelationship between problems of pure and applied mathematics and also between mathematics and physics.
Author: Minoru Wakimoto
Publisher: World Scientific
Published: 2001
Total Pages: 456
ISBN-13: 9810241291
DOWNLOAD EBOOKThe representation theory of affine Lie algebras has been developed in close connection with various areas of mathematics and mathematical physics in the last two decades. There are three excellent books on it, written by Victor G Kac. This book begins with a survey and review of the material treated in Kac's books. In particular, modular invariance and conformal invariance and are explained in more detail. The book then goes further, dealing with some of the recent topics involving the representation theory of affine Lie algebras. Since these topics are important not only in themselves but also in their application to some areas of mathematics and mathematical physics, the book expounds them with examples and detailed calculations.
Author: Victor G. Kac
Publisher: Springer Science & Business Media
Published: 2013-11-09
Total Pages: 267
ISBN-13: 1475713827
DOWNLOAD EBOOKAuthor: Gerard G. A. Bäuerle
Publisher: North Holland
Published: 1990
Total Pages: 420
ISBN-13:
DOWNLOAD EBOOKThis 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: Neelacanta Sthanumoorthy
Publisher: Academic Press
Published: 2016-04-26
Total Pages: 514
ISBN-13: 012804683X
DOWNLOAD EBOOKLie 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
Author: Gerard G. A. Bäuerle
Publisher:
Published: 1990
Total Pages: 578
ISBN-13:
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