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Lie Groups, Lie Algebras, and Some of Their Applications
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Robert Gilmore
With rigor and clarity, this upper-level undergraduate text employs numerous exercises, solved problems, and figures to introduce upper-level undergraduates to Lie group theory and physical applications. It further illustrates Lie group theory's role in expressing concepts and results from several fields of physics. 1974 edition. Includes 75 ...
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Lie Groups: An Approach Through Invariants and Representations
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by
Claudio Procesi
Lie groups has been an increasing area of focus and rich research since the middle of the 20th century. Procesi's masterful approach to Lie groups through invariants and representations gives the reader a comprehensive treatment of the classical groups along with an extensive introduction to a wide range of topics associated with Lie groups: ...
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Foundations of differentiable manifolds and Lie groups
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Frank Wilson Warner
Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. It includes differentiable manifolds, tensors and differentiable forms. Lie groups and homogenous spaces, integration on manifolds, and in addition provides a proof of the de Rham theorem via ...
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Lie Groups, Lie Algebras, and Representations: An Elementary Introduction
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Brian Hall
This book addresses Lie groups, Lie algebras, and representation theory. In order to keep the prerequisites to a minimum, the author restricts attention to matrix Lie groups and Lie algebras. This approach keeps the discussion concrete, allows the reader to get to the heart of the subject quickly, and covers all of the most interesting examples. ...
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Topics in Harmonic Analysis: Related to the Littlewood-Paley Theory
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Elias M. Stein
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Lie Groups
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by
Daniel Bump
This book is intended for a one year graduate course on Lie groups and Lie algebras. The author proceeds 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. For compact Lie groups, the Peter-Weyl theorem, conjugacy of ...
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Naive Lie Theory
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by
John Stillwell
In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called 'classical groups' that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, ...
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Acoustics and the Performance of Music: Manual for Acousticians, Audio Engineers, Musicians, Architects and Musical Instruments Makers
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Jurgen Meyer, MD, Uwe Hansen (Translator)
The objective of the book is to focus insights in the field of Acoustics of Musical Instruments, Room-Acoustics and Psycho-Acoustics on applications in musical performance. In this context, the directional dependence of sound radiation by musical instruments and the voice, as well as questions of concert hall design and room acoustical computer ...
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Differential Geometry, Lie Groups & Symmetric Spaces
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Sigurdur Helgason
From reviews for the First Edition: 'A great book...a necessary item in any mathematical library' - S. S. Chern. The study of homogeneous spaces provides excellent insights into both differential geometry and Lie groups. In geometry, for instance, general theorems and properties will also hold for homogeneous spaces, and will usually be easier to ...
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Algebraic Methods in Quantum Chemistry and Physics
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by
Francisco M Fernandez, Eduardo A Castro
"Algebraic Methods in Quantum Chemistry and Physics" provides straightforward presentations of selected topics in theoretical chemistry and physics, including Lie algebras and their applications, harmonic oscillators, bilinear oscillators, perturbation theory, numerical solutions of the Schrodinger equation, and parameterizations of the time ...
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The Orbit Method in Representation PM'82
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by
Dulfo, Pederson, Vergne
Ever since its introduction around 1960 by Kirillov, the orbit method has played a major role in representation theory of Lie groups and Lie algebras. This book contains the proceedings of a conference held from August 29 to September 2, 1988, at the University of Copenhagen, about 'the orbit method in representation theory'. It contains ten ...
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Harmonic Analysis on the Heisenberg Group
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by
Sundaram Thangavelu
The Heisenberg group plays an important role in several branches of mathematics, such as representation theory, partial differential equations, number theory, several complex variables and quantum mechanics. This monograph deals with various aspects of harmonic analysis on the Heisenberg group, which is the most commutative among the non ...
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Lie algebras and lie groups 1964 lectures given at Harvard University
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by
Serre
This book reproduces J-P Serre's 1964 Harvard lectures. The aim is to introduce the reader to the "Lie dictionary: Lie algebras and Lie groups". Special features of the presentation are its emphasis on formal groups (in the Lie group part) and the use of analytic manifolds on p-adic fields. Some knowledge of algebra and calculus is required of the ...
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Emergence of the Theory of Lie Groups
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by
Thomas Hawkins
Written by the recipient of the 1997 MAA Chauvenet Prize for mathematical exposition, this book tells how the theory of Lie groups emerged from a fascinating cross fertilization of many strains of 19th and early 20th century geometry, analysis, mathematical physics, algebra and topology. The reader will meet a host of mathematicians from the ...
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Unitary Representations of Reductive Lie Groups
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David A Vogan, Jr.
This book is an expanded version of the "Hermann Weyl Lectures" given at the Institute for Advanced Study in January 1986. It outlines some of what is now known about irreducible unitary representations of real reductive groups, providing fairly complete definitions and references, and sketches (at least) of most proofs. The first half of the book ...
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Ratner's Theorems on Unipotent Flows
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by
Dave Witte Morris
The theorems of Berkeley mathematician, Marina Ratner have guided key advances in the understanding of dynamical systems. Unipotent flows are well-behaved dynamical systems, and Ratner has shown that the closure of every orbit for such a flow is of a simple algebraic or geometric form. In "Ratner's Theorems on Unipotent Flows", Dave Witte Morris ...
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Introduction to Lie Algebras and Representation Theory
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by
James E Humphreys
This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, Euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some ...
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Livy Processes in Lie Groups
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by
Ming Liao, Bela Bollobas (Editor), W Fulton (Editor)
The theory of Levy processes in Lie groups is not merely an extension of the theory of Levy processes in Euclidean spaces. Because of the unique structures possessed by non-commutative Lie groups, these processes exhibit certain interesting limiting properties which are not present for their counterparts in Euclidean spaces. These properties ...
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Lie Groups and Lie Algebras: Chapters 4-6
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by
Nicolas Bourbaki, A Pressley (Translator)
From the reviews of the French edition: 'This is a rich and useful volume. The material it treats has relevance well beyond the theory of Lie groups and algebras, ranging from the geometry of regular polytopes and paving problems to current work on finite simple groups having a (B,N)-pair structure, or 'Tits systems'. A historical note provides a ...
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Noncommutative Harmonic Analysis: In Honor of Jacques Carmona
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Patrick Delorme (Editor), Michele Vergne, Michhle Vergne (Editor)
This volume is devoted to the theme of Noncommutative Harmonic Analysis and consists of articles in honor of Jacques Carmona, whose scientific interests range through all aspects of Lie group representations. The topics encompass the theory of representations of reductive Lie groups, and especially the determination of the unitary dual, the ...
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Geometry and Representation Theory of Real and P-Adic Lie Groups
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by
Juan Tirao (Editor), David A Vogan, Jr. (Editor), Joe Wolf (Editor)
This text provides a thorough introduction to the more active parts of representation theory and to some of its ongoing applications.
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An introduction to harmonic analysis on semisimple Lie groups
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by
Varadarajan
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 subject ...
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Lie groups for pedestrians
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by
Harry J. Lipkin
This book shows how well-known methods of angular momentum algebra can be extended to treat other Lie groups. Chapters cover isospin, the three-dimensional harmonic oscillator, Young diagrams, more. 1966 edition.
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Abstract Root Subgroups and Simple Groups of Lie-Type
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by
Franz Georg Timmesfeld
The present book is the first to systematically treat the theory of groups generated by a conjugacy class of subgroups, satisfying certain generational properties on pairs of subgroups. For finite groups, this theory has been developed in the 1970s mainly by M. Aschbacher, B. Fischer and the author. It was extended to arbitrary groups in the 1990s ...
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Introduction to Lie Groups and Lie Algebras
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by
Arthur A Sagle, Ralph E Walde
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