Characters Of Connected Lie Groups

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Characters of Connected Lie Groups

L. Pukanszky
Characters of Connected Lie Groups Book PDF

Author : L. Pukanszky
Publisher : American Mathematical Soc.
Page : 149 pages
File Size : 42,6 Mb
Release : 1999
Category : Characters of groups
ISBN : 9780821810880

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Characters of Connected Lie Groups by L. Pukanszky Pdf

This book adds to the great body of research that extends back to A. Weil and E. P. Wigner on the unitary representations of locally compact groups and their characters, i.e. the interplay between classical group theory and modern analysis. The groups studied here are the connected Lie groups of general type (not necessarily nilpotent or semisimple). Final results reflect Kirillov's orbit method; in the case of groups that may be non-algebraic or non-type I, the method requires considerable sophistication. Methods used range from deep functional analysis (the theory of $C*$-algebras, factors from F. J. Murray and J. von Neumann, and measure theory) to differential geometry (Lie groups and Hamiltonian actions). This book presents for the first time a systematic and concise compilation of proofs previously dispersed throughout the literature. The result is an impressive example of the deepness of Pukanszky's work.

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 : 40,5 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

Symmetries, Lie Algebras and Representations

Jürgen Fuchs,Christoph Schweigert
Symmetries Lie Algebras and Representations Book PDF

Author : Jürgen Fuchs,Christoph Schweigert
Publisher : Cambridge University Press
Page : 464 pages
File Size : 44,6 Mb
Release : 2003-10-07
Category : Mathematics
ISBN : 0521541190

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Symmetries, Lie Algebras and Representations by Jürgen Fuchs,Christoph Schweigert Pdf

This book gives an introduction to Lie algebras and their representations. Lie algebras have many applications in mathematics and physics, and any physicist or applied mathematician must nowadays be well acquainted with them.

Representations of Compact Lie Groups

T. Bröcker,T.tom Dieck
Representations of Compact Lie Groups Book PDF

Author : T. Bröcker,T.tom Dieck
Publisher : Springer Science & Business Media
Page : 323 pages
File Size : 44,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662129180

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Representations of Compact Lie Groups by T. Bröcker,T.tom Dieck Pdf

This introduction to the representation theory of compact Lie groups follows Herman Weyl’s original approach. It discusses all aspects of finite-dimensional Lie theory, consistently emphasizing the groups themselves. Thus, the presentation is more geometric and analytic than algebraic. It is a useful reference and a source of explicit computations. Each section contains a range of exercises, and 24 figures help illustrate geometric concepts.

Lie Groups, Lie Algebras, and Representations

Brian Hall
Lie Groups Lie Algebras and Representations Book PDF

Author : Brian Hall
Publisher : Springer
Page : 452 pages
File Size : 51,9 Mb
Release : 2015-05-11
Category : Mathematics
ISBN : 9783319134673

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

This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula. Review of the first edition: This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended. — The Mathematical Gazette

Applications of Lie Groups to Differential Equations

Peter J. Olver
Applications of Lie Groups to Differential Equations Book PDF

Author : Peter J. Olver
Publisher : Springer Science & Business Media
Page : 524 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468402742

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Applications of Lie Groups to Differential Equations by Peter J. Olver Pdf

This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.

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 : 41,9 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.

An Introduction to Harmonic Analysis on Semisimple Lie Groups

V. S. Varadarajan
An Introduction to Harmonic Analysis on Semisimple Lie Groups Book PDF

Author : V. S. Varadarajan
Publisher : Cambridge University Press
Page : 326 pages
File Size : 52,7 Mb
Release : 1999-07-22
Category : Mathematics
ISBN : 0521663628

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An Introduction to Harmonic Analysis on Semisimple Lie Groups by V. S. Varadarajan Pdf

Now in paperback, this graduate-level textbook is an introduction to the representation theory of semi-simple Lie groups. As such, it will be suitable for research students in algebra and analysis, and for research mathematicians requiring a readable account of the topic. The author emphasizes the development of the central themes of the sunject in the context of special examples, without losing sight of its general flow and structure. The book concludes with appendices sketching some basic topics with a comprehensive guide to further reading.

Representation Theory of Lie Groups

Jeffrey Adams, David Vogan
Representation Theory of Lie Groups Book PDF

Author : Jeffrey Adams, David Vogan
Publisher : American Mathematical Soc.
Page : 340 pages
File Size : 44,5 Mb
Release : 2015-06-02
Category : Electronic
ISBN : 9781470423148

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Representation Theory of Lie Groups by Jeffrey Adams, David Vogan Pdf

This book contains written versions of the lectures given at the PCMI Graduate Summer School on the representation theory of Lie groups. The volume begins with lectures by A. Knapp and P. Trapa outlining the state of the subject around the year 1975, specifically, the fundamental results of Harish-Chandra on the general structure of infinite-dimensional representations and the Langlands classification. Additional contributions outline developments in four of the most active areas of research over the past 20 years. The clearly written articles present results to date, as follows: R. Zierau and L. Barchini discuss the construction of representations on Dolbeault cohomology spaces. D. Vogan describes the status of the Kirillov-Kostant "philosophy of coadjoint orbits" for unitary representations. K. Vilonen presents recent advances in the Beilinson-Bernstein theory of "localization". And Jian-Shu Li covers Howe's theory of "dual reductive pairs". Each contributor to the volume presents the topics in a unique, comprehensive, and accessible manner geared toward advanced graduate students and researchers. Students should have completed the standard introductory graduate courses for full comprehension of the work. The book would also serve well as a supplementary text for a course on introductory infinite-dimensional representation theory. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Lie Groups

J.J. Duistermaat,Johan A.C. Kolk
Lie Groups Book PDF

Author : J.J. Duistermaat,Johan A.C. Kolk
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 40,7 Mb
Release : 1999-12-15
Category : Mathematics
ISBN : 3540152938

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Lie Groups by J.J. Duistermaat,Johan A.C. Kolk Pdf

This (post) graduate text gives a broad introduction to Lie groups and algebras with an emphasis on differential geometrical methods. It analyzes the structure of compact Lie groups in terms of the action of the group on itself by conjugation, culminating in the classification of the representations of compact Lie groups and their realization as sections of holomorphic line bundles over flag manifolds. Appendices provide background reviews.

Harmonic Analysis on Exponential Solvable Lie Groups

Hidenori Fujiwara,Jean Ludwig
Harmonic Analysis on Exponential Solvable Lie Groups Book PDF

Author : Hidenori Fujiwara,Jean Ludwig
Publisher : Springer
Page : 465 pages
File Size : 51,8 Mb
Release : 2014-12-05
Category : Mathematics
ISBN : 9784431552888

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Harmonic Analysis on Exponential Solvable Lie Groups by Hidenori Fujiwara,Jean Ludwig Pdf

This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. There still are many interesting open problems, and the book contributes to the future progress of this research field. As well, various related topics are presented to motivate young researchers. The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups. This method tells us that the unitary dual of these groups is realized as the space of their coadjoint orbits. This fact is established using the Mackey theory for induced representations, and that mechanism is explained first. One of the fundamental problems in the representation theory is the irreducible decomposition of induced or restricted representations. Therefore, these decompositions are studied in detail before proceeding to various related problems: the multiplicity formula, Plancherel formulas, intertwining operators, Frobenius reciprocity, and associated algebras of invariant differential operators. The main reasoning in the proof of the assertions made here is induction, and for this there are not many tools available. Thus a detailed analysis of the objects listed above is difficult even for exponential solvable Lie groups, and it is often assumed that G is nilpotent. To make the situation clearer and future development possible, many concrete examples are provided. Various topics presented in the nilpotent case still have to be studied for solvable Lie groups that are not nilpotent. They all present interesting and important but difficult problems, however, which should be addressed in the near future. Beyond the exponential case, holomorphically induced representations introduced by Auslander and Kostant are needed, and for that reason they are included in this book.

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 : 43,7 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 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 : 40,8 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.

Representation Theory of Lie Groups

M. F. Atiyah
Representation Theory of Lie Groups Book PDF

Author : M. F. Atiyah
Publisher : Cambridge University Press
Page : 349 pages
File Size : 48,8 Mb
Release : 1979
Category : Mathematics
ISBN : 9780521226363

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Representation Theory of Lie Groups by M. F. Atiyah Pdf

In 1977 a symposium was held in Oxford to introduce Lie groups and their representations to non-specialists.

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 : 42,5 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.