Lie Groups Lie Algebras And Cohomology Mn 34 Volume 34

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Lie Groups, Lie Algebras, and Cohomology. (MN-34), Volume 34

Anthony W. Knapp
Lie Groups Lie Algebras and Cohomology MN 34 Volume 34 Book PDF

Author : Anthony W. Knapp
Publisher : Princeton University Press
Page : 526 pages
File Size : 43,8 Mb
Release : 2021-01-12
Category : Mathematics
ISBN : 9780691223803

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Lie Groups, Lie Algebras, and Cohomology. (MN-34), Volume 34 by Anthony W. Knapp Pdf

This book starts with the elementary theory of Lie groups of matrices and arrives at the definition, elementary properties, and first applications of cohomological induction, which is a recently discovered algebraic construction of group representations. Along the way it develops the computational techniques that are so important in handling Lie groups. The book is based on a one-semester course given at the State University of New York, Stony Brook in fall, 1986 to an audience having little or no background in Lie groups but interested in seeing connections among algebra, geometry, and Lie theory. These notes develop what is needed beyond a first graduate course in algebra in order to appreciate cohomological induction and to see its first consequences. Along the way one is able to study homological algebra with a significant application in mind; consequently one sees just what results in that subject are fundamental and what results are minor.

Lie Groups, Lie Algebras, and Cohomology

Anthony W. Knapp
Lie Groups Lie Algebras and Cohomology Book PDF

Author : Anthony W. Knapp
Publisher : Princeton University Press
Page : 522 pages
File Size : 49,9 Mb
Release : 1988-05-21
Category : Mathematics
ISBN : 9780691084985

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Lie Groups, Lie Algebras, and Cohomology by Anthony W. Knapp Pdf

This book starts with the elementary theory of Lie groups of matrices and arrives at the definition, elementary properties, and first applications of cohomological induction, which is a recently discovered algebraic construction of group representations. Along the way it develops the computational techniques that are so important in handling Lie groups. The book is based on a one-semester course given at the State University of New York, Stony Brook in fall, 1986 to an audience having little or no background in Lie groups but interested in seeing connections among algebra, geometry, and Lie theory. These notes develop what is needed beyond a first graduate course in algebra in order to appreciate cohomological induction and to see its first consequences. Along the way one is able to study homological algebra with a significant application in mind; consequently one sees just what results in that subject are fundamental and what results are minor.

Lie Groups Beyond an Introduction

Anthony W. Knapp
Lie Groups Beyond an Introduction Book PDF

Author : Anthony W. Knapp
Publisher : Springer Science & Business Media
Page : 622 pages
File Size : 41,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475724530

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Lie Groups Beyond an Introduction by Anthony W. Knapp Pdf

Lie Groups Beyond an Introduction takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. A feature of the presentation is that it encourages the reader's comprehension of Lie group theory to evolve from beginner to expert: initial insights make use of actual matrices, while later insights come from such structural features as properties of root systems, or relationships among subgroups, or patterns among different subgroups.

Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics

Josi A. de Azcárraga,Josi M. Izquierdo
Lie Groups Lie Algebras Cohomology and Some Applications in Physics Book PDF

Author : Josi A. de Azcárraga,Josi M. Izquierdo
Publisher : Cambridge University Press
Page : 480 pages
File Size : 44,9 Mb
Release : 1998-08-06
Category : Mathematics
ISBN : 0521597005

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Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics by Josi A. de Azcárraga,Josi M. Izquierdo Pdf

A self-contained introduction to the cohomology theory of Lie groups and some of its applications in physics.

Lie Groups, Lie Algebras, and Their Representations

V.S. Varadarajan
Lie Groups Lie Algebras and Their Representations Book PDF

Author : V.S. Varadarajan
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 42,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781461211266

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Lie Groups, Lie Algebras, and Their Representations by V.S. Varadarajan Pdf

This book has grown out of a set of lecture notes I had prepared for a course on Lie groups in 1966. When I lectured again on the subject in 1972, I revised the notes substantially. It is the revised version that is now appearing in book form. The theory of Lie groups plays a fundamental role in many areas of mathematics. There are a number of books on the subject currently available -most notably those of Chevalley, Jacobson, and Bourbaki-which present various aspects of the theory in great depth. However, 1 feei there is a need for a single book in English which develops both the algebraic and analytic aspects of the theory and which goes into the representation theory of semi simple Lie groups and Lie algebras in detail. This book is an attempt to fiii this need. It is my hope that this book will introduce the aspiring graduate student as well as the nonspecialist mathematician to the fundamental themes of the subject. I have made no attempt to discuss infinite-dimensional representations. This is a very active field, and a proper treatment of it would require another volume (if not more) of this size. However, the reader who wants to take up this theory will find that this book prepares him reasonably well for that task.

Lie Groups and Algebraic Groups

Arkadij L. Onishchik,Ernest B. Vinberg
Lie Groups and Algebraic Groups Book PDF

Author : Arkadij L. Onishchik,Ernest B. Vinberg
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642743344

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Lie Groups and Algebraic Groups by Arkadij L. Onishchik,Ernest B. Vinberg Pdf

This book is based on the notes of the authors' seminar on algebraic and Lie groups held at the Department of Mechanics and Mathematics of Moscow University in 1967/68. Our guiding idea was to present in the most economic way the theory of semisimple Lie groups on the basis of the theory of algebraic groups. Our main sources were A. Borel's paper [34], C. ChevalIey's seminar [14], seminar "Sophus Lie" [15] and monographs by C. Chevalley [4], N. Jacobson [9] and J-P. Serre [16, 17]. In preparing this book we have completely rearranged these notes and added two new chapters: "Lie groups" and "Real semisimple Lie groups". Several traditional topics of Lie algebra theory, however, are left entirely disregarded, e.g. universal enveloping algebras, characters of linear representations and (co)homology of Lie algebras. A distinctive feature of this book is that almost all the material is presented as a sequence of problems, as it had been in the first draft of the seminar's notes. We believe that solving these problems may help the reader to feel the seminar's atmosphere and master the theory. Nevertheless, all the non-trivial ideas, and sometimes solutions, are contained in hints given at the end of each section. The proofs of certain theorems, which we consider more difficult, are given directly in the main text. The book also contains exercises, the majority of which are an essential complement to the main contents.

Lie Groups and Lie Algebras III

A.L. Onishchik,E.B. Vinberg
Lie Groups and Lie Algebras III Book PDF

Author : A.L. Onishchik,E.B. Vinberg
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 43,5 Mb
Release : 1994-07-12
Category : Mathematics
ISBN : 3540546839

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Lie Groups and Lie Algebras III by A.L. Onishchik,E.B. Vinberg Pdf

A comprehensive and modern account of the structure and classification of Lie groups and finite-dimensional Lie algebras, by internationally known specialists in the field. This Encyclopaedia volume will be immensely useful to graduate students in differential geometry, algebra and theoretical physics.

Lie Theory

Jean-Philippe Anker,Bent Orsted
Lie Theory Book PDF

Author : Jean-Philippe Anker,Bent Orsted
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 45,6 Mb
Release : 2004
Category : Mathematics
ISBN : 0817633731

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Lie Theory by Jean-Philippe Anker,Bent Orsted Pdf

* First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians. * Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." * Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations. * Should benefit graduate students and researchers in mathematics and mathematical physics.

An Introduction to Lie Groups and Lie Algebras

Alexander A. Kirillov
An Introduction to Lie Groups and Lie Algebras Book PDF

Author : Alexander A. Kirillov
Publisher : Cambridge University Press
Page : 237 pages
File Size : 41,9 Mb
Release : 2008-07-31
Category : Mathematics
ISBN : 9780521889698

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An Introduction to Lie Groups and Lie Algebras by Alexander A. Kirillov Pdf

Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples

Lie Groups and Lie Algebras I

V.V. Gorbatsevich,A.L. Onishchik,E.B. Vinberg
Lie Groups and Lie Algebras I Book PDF

Author : V.V. Gorbatsevich,A.L. Onishchik,E.B. Vinberg
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 41,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642579998

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Lie Groups and Lie Algebras I by V.V. Gorbatsevich,A.L. Onishchik,E.B. Vinberg Pdf

From the reviews: "..., the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source, ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" --The New Zealand Mathematical Society Newsletter

Lie Groups and Lie Algebras II

A.L. Onishchik
Lie Groups and Lie Algebras II Book PDF

Author : A.L. Onishchik
Publisher : Boom Koninklijke Uitgevers
Page : 238 pages
File Size : 45,6 Mb
Release : 2000-02-03
Category : Mathematics
ISBN : 3540505857

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Lie Groups and Lie Algebras II by A.L. Onishchik Pdf

A systematic survey of all the basic results on the theory of discrete subgroups of Lie groups, presented in a convenient form for users. The book makes the theory accessible to a wide audience, and will be a standard reference for many years to come.

Lie Groups, Lie Algebras, and Representations

Brian C. Hall
Lie Groups Lie Algebras and Representations Book PDF

Author : Brian C. Hall
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 49,8 Mb
Release : 2003-08-07
Category : Mathematics
ISBN : 0387401229

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Lie Groups, Lie Algebras, and Representations by Brian C. Hall Pdf

This book provides an introduction to Lie groups, Lie algebras, and repre sentation theory, aimed at graduate students in mathematics and physics. Although there are already several excellent books that cover many of the same topics, this book has two distinctive features that I hope will make it a useful addition to the literature. First, it treats Lie groups (not just Lie alge bras) in a way that minimizes the amount of manifold theory needed. Thus, I neither assume a prior course on differentiable manifolds nor provide a con densed such course in the beginning chapters. Second, this book provides a gentle introduction to the machinery of semi simple groups and Lie algebras by treating the representation theory of SU(2) and SU(3) in detail before going to the general case. This allows the reader to see roots, weights, and the Weyl group "in action" in simple cases before confronting the general theory. The standard books on Lie theory begin immediately with the general case: a smooth manifold that is also a group. The Lie algebra is then defined as the space of left-invariant vector fields and the exponential mapping is defined in terms of the flow along such vector fields. This approach is undoubtedly the right one in the long run, but it is rather abstract for a reader encountering such things for the first time.

Lie Groups, Lie Algebras

Melvin Hausner,Jacob T. Schwartz
Lie Groups Lie Algebras Book PDF

Author : Melvin Hausner,Jacob T. Schwartz
Publisher : CRC Press
Page : 242 pages
File Size : 47,5 Mb
Release : 1968
Category : Lie algebras
ISBN : 9780677002804

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Lie Groups, Lie Algebras by Melvin Hausner,Jacob T. Schwartz Pdf

Polished lecture notes provide a clean and usefully detailed account of the standard elements of the theory of Lie groups and algebras. Following nineteen pages of preparatory material, Part I (seven brief chapters) treats "Lie groups and their Lie algebras"; Part II (seven chapters) treats "complex semi-simple Lie algebras"; Part III (two chapters) treats "real semi-simple Lie algebras". The page design is intimidatingly dense, the exposition very much in the familiar "definition/lemma/proof/theorem/proof/remark" mode, and there are no exercises or bibliography. (NW) Annotation copyrighted by Book News, Inc., Portland, OR

Lie Groups, Lie Algebras, and Some of Their Applications

Robert Gilmore
Lie Groups Lie Algebras and Some of Their Applications Book PDF

Author : Robert Gilmore
Publisher : Courier Corporation
Page : 610 pages
File Size : 48,8 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486131566

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Lie Groups, Lie Algebras, and Some of Their Applications by Robert Gilmore Pdf

This text introduces upper-level undergraduates to Lie group theory and physical applications. It further illustrates Lie group theory's role in several fields of physics. 1974 edition. Includes 75 figures and 17 tables, exercises and problems.

Noncompact Lie Groups and Some of Their Applications

Elizabeth A. Tanner,R. Wilson
Noncompact Lie Groups and Some of Their Applications Book PDF

Author : Elizabeth A. Tanner,R. Wilson
Publisher : Springer Science & Business Media
Page : 493 pages
File Size : 52,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401110785

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Noncompact Lie Groups and Some of Their Applications by Elizabeth A. Tanner,R. Wilson Pdf

During the past two decades representations of noncompact Lie groups and Lie algebras have been studied extensively, and their application to other branches of mathematics and to physical sciences has increased enormously. Several theorems which were proved in the abstract now carry definite mathematical and physical sig nificance. Several physical observations which were not understood before are now explained in terms of models based on new group-theoretical structures such as dy namical groups and Lie supergroups. The workshop was designed to bring together those mathematicians and mathematical physicists who are actively working in this broad spectrum of research and to provide them with the opportunity to present their recent results and to discuss the challenges facing them in the many problems that remain. The objective of the workshop was indeed well achieved. This book contains 31 lectures presented by invited participants attending the NATO Advanced Research Workshop held in San Antonio, Texas, during the week of January 3-8, 1993. The introductory article by the editors provides a brief review of the concepts underlying these lectures (cited by author [*]) and mentions some of their applications. The articles in the book are grouped under the following general headings: Lie groups and Lie algebras, Lie superalgebras and Lie supergroups, and Quantum groups, and are arranged in the order in which they are cited in the introductory article. We are very thankful to Dr.