Lie Groups Lie Algebras And Some Of Their Applications
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Lie Groups Lie Algebras And Some Of Their Applications
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Author : Robert Gilmore
language : en
Publisher: Courier Corporation
Release Date : 2012-05-23
Lie Groups Lie Algebras And Some Of Their Applications written by Robert Gilmore and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-23 with Mathematics categories.
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.
Lie Groups Lie Algebras And Some Of Their Applications
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Author : Robert Gilmore
language : en
Publisher: Courier Corporation
Release Date : 2006-01-04
Lie Groups Lie Algebras And Some Of Their Applications written by Robert Gilmore and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-04 with Mathematics categories.
An opening discussion of introductory concepts leads to explorations of the classical groups, continuous groups and Lie groups, and Lie groups and Lie algebras. Some simple but illuminating examples are followed by examinations of classical algebras, Lie algebras and root spaces, root spaces and Dynkin diagrams, real forms, and contractions and expansions.
Noncompact Lie Groups And Some Of Their Applications
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Author : Elizabeth A. Tanner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Noncompact Lie Groups And Some Of Their Applications written by Elizabeth A. Tanner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Lie Algebras And Applications
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Author : Francesco Iachello
language : en
Publisher: Springer
Release Date : 2007-02-22
Lie Algebras And Applications written by Francesco Iachello and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-22 with Science categories.
This book, designed for advanced graduate students and post-graduate researchers, introduces Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. The book contains many examples that help to elucidate the abstract algebraic definitions. It provides a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators and the dimensions of the representations of all classical Lie algebras.
Lie Groups Lie Algebras Cohomology And Some Applications In Physics
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Author : Josi A. de Azcárraga
language : en
Publisher: Cambridge University Press
Release Date : 1998-08-06
Lie Groups Lie Algebras Cohomology And Some Applications In Physics written by Josi A. de Azcárraga and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-08-06 with Mathematics categories.
A self-contained introduction to the cohomology theory of Lie groups and some of its applications in physics.
Lie Groups And Algebras With Applications To Physics Geometry And Mechanics
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Author : D.H. Sattinger
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Lie Groups And Algebras With Applications To Physics Geometry And Mechanics written by D.H. Sattinger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
This book is intended as an introductory text on the subject of Lie groups and algebras and their role in various fields of mathematics and physics. It is written by and for researchers who are primarily analysts or physicists, not algebraists or geometers. Not that we have eschewed the algebraic and geo metric developments. But we wanted to present them in a concrete way and to show how the subject interacted with physics, geometry, and mechanics. These interactions are, of course, manifold; we have discussed many of them here-in particular, Riemannian geometry, elementary particle physics, sym metries of differential equations, completely integrable Hamiltonian systems, and spontaneous symmetry breaking. Much ofthe material we have treated is standard and widely available; but we have tried to steer a course between the descriptive approach such as found in Gilmore and Wybourne, and the abstract mathematical approach of Helgason or Jacobson. Gilmore and Wybourne address themselves to the physics community whereas Helgason and Jacobson address themselves to the mathematical community. This book is an attempt to synthesize the two points of view and address both audiences simultaneously. We wanted to present the subject in a way which is at once intuitive, geometric, applications oriented, mathematically rigorous, and accessible to students and researchers without an extensive background in physics, algebra, or geometry.
Lie Groups Lie Algebras
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Author : Melvin Hausner
language : en
Publisher: CRC Press
Release Date : 1968
Lie Groups Lie Algebras written by Melvin Hausner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Lie algebras categories.
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
Applications Of Lie Groups To Differential Equations
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Author : Peter J. Olver
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applications Of Lie Groups To Differential Equations written by Peter J. Olver and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
A Survey Of Lie Groups And Lie Algebras With Applications And Computational Methods
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Author : Johan G. F. Belinfante
language : en
Publisher: SIAM
Release Date : 1989-01-01
A Survey Of Lie Groups And Lie Algebras With Applications And Computational Methods written by Johan G. F. Belinfante and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Mathematics categories.
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.
Lie Groups Lie Algebras And Cohomology
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Author : Anthony W. Knapp
language : en
Publisher: Princeton University Press
Release Date : 1988-05-21
Lie Groups Lie Algebras And Cohomology written by Anthony W. Knapp and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-05-21 with Mathematics categories.
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.