A Survey Of Lie Groups And Lie Algebras With Applications And Computational Methods

Author : Johan G. F. Belinfante,Bernard Kolman
Publisher : SIAM
Page : 175 pages
File Size : 50,7 Mb
Release : 1989-01-01
Category : Mathematics
ISBN : 1611971330

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A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods by Johan G. F. Belinfante,Bernard Kolman Pdf

Introduces the concepts and methods of the Lie theory in a form accessible to the non-specialist by keeping mathematical prerequisites to a minimum. Although the authors have concentrated on presenting results while omitting most of the proofs, they have compensated for these omissions by including many references to the original literature. Their treatment is directed toward the reader seeking a broad view of the subject rather than elaborate information about technical details. Illustrations of various points of the Lie theory itself are found throughout the book in material on applications. In this reprint edition, the authors have resisted the temptation of including additional topics. Except for correcting a few minor misprints, the character of the book, especially its focus on classical representation theory and its computational aspects, has not been changed.

Author : Anthony W. Knapp
Publisher : Princeton University Press
Page : 522 pages
File Size : 50,9 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.

Author : Bernard Kolman
Publisher : Unknown
Page : 176 pages
File Size : 54,6 Mb
Release : 1973
Category : Lie algebras
ISBN : STANFORD:36105031839942

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Lie Algebras: Applications and Computational Methods by Bernard Kolman Pdf

Author : Anthony W. Knapp
Publisher : Princeton University Press
Page : 526 pages
File Size : 54,9 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.

Author : Johan G. F. Belinfante,Bernard Kolman
Publisher : SIAM
Page : 168 pages
File Size : 50,8 Mb
Release : 1989-01-01
Category : Mathematics
ISBN : 9780898712438

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A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods by Johan G. F. Belinfante,Bernard Kolman Pdf

In this reprint edition, the character of the book, especially its focus on classical representation theory and its computational aspects, has not been changed

Author : Bernard Kolman
Publisher : Society for Industrial and Applied Mathematics (SIAM)
Page : 155 pages
File Size : 44,9 Mb
Release : 1973-12
Category : Lie algebras
ISBN : 0898711533

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Lie Algebras by Bernard Kolman Pdf

Author : Jean-Philippe Anker,Bent Orsted
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681920

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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.

Author : Melvin Hausner,Jacob T. Schwartz
Publisher : CRC Press
Page : 242 pages
File Size : 54,8 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

Author : Ljudmila A Bordag
Publisher : World Scientific Publishing Company
Page : 340 pages
File Size : 48,7 Mb
Release : 2015-05-27
Category : Mathematics
ISBN : 9789814667265

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Geometrical Properties of Differential Equations by Ljudmila A Bordag Pdf

This textbook is a short comprehensive and intuitive introduction to Lie group analysis of ordinary and partial differential equations. This practical-oriented material contains a large number of examples and problems accompanied by detailed solutions and figures. In comparison with the known beginner guides to Lie group analysis, the book is oriented toward students who are interested in financial mathematics, mathematical finance and economics. We provide the results of the Lie group analysis of actual models in Financial Mathematics using recent publications. These models are usually formulated as nonlinear partial differential equations and are rather difficult to make use of. With the help of Lie group analysis it is possible to describe some important properties of these models and to obtain interesting reductions in a clear and understandable algorithmic way. The book can serve as a short introduction for a further study of modern geometrical analysis applied to models in financial mathematics. It can also be used as textbook in a master's program, in an intensive compact course, or for self study. The textbook with a large number of examples will be useful not only for students who are interested in Financial Mathematics but also for people who are working in other areas of research that are not directly connected with Physics (for instance in such areas of Applied Mathematics like mathematical economy, bio systems, coding theory, etc.).

Author : Daniel Bump
Publisher : Springer Science & Business Media
Page : 551 pages
File Size : 41,5 Mb
Release : 2013-10-01
Category : Mathematics
ISBN : 9781461480242

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Lie Groups by Daniel Bump Pdf

This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes beyond the representation theory of compact Lie groups, which is the basis of many texts, and provides a carefully chosen range of material to give the student the bigger picture. The book is organized to allow different paths through the material depending on one's interests. This second edition has substantial new material, including improved discussions of underlying principles, streamlining of some proofs, and many results and topics that were not in the first edition. For compact Lie groups, the book covers the Peter–Weyl theorem, Lie algebra, conjugacy of maximal tori, the Weyl group, roots and weights, Weyl character formula, the fundamental group and more. The book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flag varieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin. Other topics that are treated are symmetric function theory, the representation theory of the symmetric group, Frobenius–Schur duality and GL(n) × GL(m) duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatorics of tableaux, Gelfand pairs, Hecke algebras, the "philosophy of cusp forms" and the cohomology of Grassmannians. An appendix introduces the reader to the use of Sage mathematical software for Lie group computations.

Author : Elizabeth A. Tanner,R. Wilson
Publisher : Springer Science & Business Media
Page : 493 pages
File Size : 50,6 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.

Author : Nail H. Ibragimov
Publisher : CRC Press
Page : 572 pages
File Size : 40,6 Mb
Release : 1995-10-24
Category : Mathematics
ISBN : 0849394198

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CRC Handbook of Lie Group Analysis of Differential Equations by Nail H. Ibragimov Pdf

Today Lie group theoretical approach to differential equations has been extended to new situations and has become applicable to the majority of equations that frequently occur in applied sciences. Newly developed theoretical and computational methods are awaiting application. Students and applied scientists are expected to understand these methods. Volume 3 and the accompanying software allow readers to extend their knowledge of computational algebra. Written by the world's leading experts in the field, this up-to-date sourcebook covers topics such as Lie-Bäcklund, conditional and non-classical symmetries, approximate symmetry groups for equations with a small parameter, group analysis of differential equations with distributions, integro-differential equations, recursions, and symbolic software packages. The text provides an ideal introduction to modern group analysis and addresses issues to both beginners and experienced researchers in the application of Lie group methods.

Author : V.S. Varadarajan
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 51,5 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.

Author : Hossein Abbaspour,Martin Moskowitz
Publisher : World Scientific Publishing Company
Page : 444 pages
File Size : 51,9 Mb
Release : 2007-09-21
Category : Mathematics
ISBN : 9789813101562

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Basic Lie Theory by Hossein Abbaspour,Martin Moskowitz Pdf

This volume provides a comprehensive treatment of basic Lie theory, primarily directed toward graduate study. The text is ideal for a full graduate course in Lie groups and Lie algebras. However, the book is also very usable for a variety of other courses: a one-semester course in Lie algebras, or on Haar measure and its applications, for advanced undergraduates; or as the text for one-semester graduate courses in Lie groups and symmetric spaces of non-compact type, or on lattices in Lie groups. The material is complete and detailed enough to be used for self-study; it can also serve as a reference work for professional mathematicians working in other areas. The book's utility for such a varied readership is enhanced by a diagram showing the interdependence of the separate chapters so that individual chapters and the material they depend upon can be selected, while others can be skipped. The book incorporates many of the most significant discoveries and pioneering contributions of the masters of the subject: Borel, Cartan, Chevalley, Iwasawa, Mostow, Siegel, and Weyl, among others.

Author : Anthony W. Knapp
Publisher : Springer Science & Business Media
Page : 622 pages
File Size : 49,9 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.