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Lie Groups, Lie Algebras, and Some of Their Applications
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by
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 Algebras in Particle Physics: From Isospin to Unified Theories
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by
Howard Georgi
An exciting new edition of a classic text. Howard Georgi is the co-inventor (with Sheldon Glashow) of the SU(5) theory. This extensively revised and updated edition of his classic text makes the theory of Lie groups accessible to graduate students, while offering a perspective on the way in which knowledge of such groups can provide an insight ...
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Lie Groups, Lie Algebras, and Representations: An Elementary Introduction
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by
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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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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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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Studies in Memory of Issai Schur
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Anthony Joseph (Editor), Anna Melnikov, Rudolf Rentschler (Editor)
This volume is dedicated to the memory of Issai Schur. It opens with some biographical reminiscences of the famous school he established in Berlin, his brutal dismissal by the Nazi regime and his tragic end in Palestine. This is followed by an extensive review of the extraordinary impact of his lesser known analytic work. Finally, leading ...
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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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Classical Geometries in Modern Contexts: Geometry of Real Inner Product Spaces
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Walter Benz
This book is based on real inner product spaces X of arbitrary (finite or infinite) dimension greater than or equal to 2. With natural properties of (general) translations and general distances of X euclidean, hyperbolic translations and distances, respectively, are characterized. For these spaces X also the sphere geometries of Mobius and Lie are ...
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Studies in Lie Theory: Dedicated to A. Joseph on His Sixtieth Birthday
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by
Joseph Bernstein (Editor), Vladimir Hinich (Editor), Anna Melnikov (Editor)
Dedicated to Anthony Joseph, this volume contains surveys and invited articles by leading specialists in representation theory. The focus here is on semisimple Lie algebras and quantum groups, where the impact of Joseph's work has been seminal and has changed the face of the subject. Two introductory biographical overviews of Joseph's ...
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Automorphic Forms and Lie Superalgebras
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by
Urmie Ray
A principal ingredient in the proof of the Moonshine Theorem, connecting the Monster group to modular forms, is the infinite dimensional Lie algebra of physical states of a chiral string on an orbifold of a 26 dimensional torus, called the Monster Lie algebra. It is a Borcherds-Kac-Moody Lie algebra with Lorentzian root lattice; and has an ...
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Infinite Dimensional Lie Algebras
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by
Victor G Kac
This is the third, substantially revised edition of this important monograph. The book is concerned with Kac-Moody algebras, a particular class of infinite-dimensional Lie algebras, and their representations. It is based on courses given over a number of years at MIT and in Paris, and is sufficiently self-contained and detailed to be used for ...
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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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Combinatorial Methods: Free Groups, Polynomials, and Free Algebras
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by
Vladimir Shpilrain, Alexander Mikhalev, Jie-Tai Yu
The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology at the beginning of the 20th Century. This book is divided into ...
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Quantum Groups and Lie Theory
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by
Andrew Pressley (Editor), J W S Cassels (Editor), N J Hitchin (Editor)
Since its genesis in the early 1980s, the subject of quantum groups has grown rapidly. By the late 1990s most of the foundational issues had been resolved and many of the outstanding problems clearly formulated. To take stock and to discuss the most fruitful directions for future research many of the world's leading figures in this area met at the ...
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Lie Algebras
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by
Nathan Jacobson
Definitive treatment of important subject in modern mathematics. Covers split semi-simple Lie algebras, universal enveloping algebras, classification of irreducible modules, automorphisms, simple Lie algebras over an arbitrary field, etc. Index.
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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 Distributions: Unitary Representation of Gauge Groups and Algebras
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by
Sergio Albeverio, Raphael J Hoegh-Krohn, Jean A Marion
Covering important aspects of the theory of unitary representations of nuclear Lie groups, this self-contained reference presents the general theory of energy representations and addresses various extensions of path groups and algebras. Requiring only a general knowledge of the theory of unitary representations, topological groups and elementary ...
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Complex Semisimple Lie Algebras
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by
Jean-Pierre Serre
These notes, already well known in their original French edition, give the basic theory of semisimple Lie algebras over the complex numbers including the basic classification theorem. The author begins with a summary of the general properties of nilpotent, solvable, and semisimple Lie algebras. Subsequent chapters introduce Cartan subalgebras, ...
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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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Lie Groups Beyond an Introduction
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by
Dr. Anthony W Knapp
From reviews of the first edition: 'The important feature of the present book is that it starts from the beginning (with only a very modest knowledge assumed) and covers all important topics...The book is very carefully organized [and] ends with 20 pages of useful historic comments. Such a comprehensive and carefully written treatment of ...
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Categories of symmetries and infinite-dimensional groups
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by
Neretin
For mathematicians working in group theory, the study of the many infinite-dimensional groups has been carried out in an individual and non-coherent way. For the first time, these apparently disparate groups have been placed together, in order to construct the 'big picture'. This book successfully gives an account of this - and shows how such ...
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Semi-Simple Lie Algebras & Their Representations
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by
Robert N Cahn
Designed to acquaint students of particle physics already familiar with SU(2) and SU(3) with techniques applicable to all simple Lie algebras, this text is especially suited to the study of grand unification theories. Subjects include simple roots and the Cartan matrix, the classical and exceptional Lie algebras, the Weyl group, and more. 1984 ...
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Geometric Analysis and Lie Theory in Mathematics and Physics
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by
Alan L Carey (Editor), Michael K Murray (Editor), J H Loxton (Editor)
This book brings together a selection of the best lectures from many graduate workshops held at the Australian National Institute for Theoretical Physics in Adelaide. The lectures presented here describe subjects currently of great interest, generally at the interface between mathematics and physics, and also where suitable expositions did not ...
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Lie Algebras of Finite and Affine Type
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by
Roger Carter
Lie algebras have many varied applications, both in mathematics and mathematical physics. This book provides a thorough but relaxed mathematical treatment of the subject, including both the Cartan-Killing-Weyl theory of finite dimensional simple algebras and the more modern theory of Kac-Moody algebras. Proofs are given in detail and the only ...
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