Lie Groups, Lie Algebras, and Some of Their Applications


Author: Robert Gilmore
Publisher: Courier Corporation
ISBN: 0486131564
Category: Mathematics
Page: 608
View: 8634
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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 Algebras


Author: Nathan Jacobson
Publisher: Courier Corporation
ISBN: 0486136795
Category: Mathematics
Page: 352
View: 6495
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DIVDefinitive 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. /div

Theory of Lie Groups


Author: Claude Chevalley
Publisher: Courier Dover Publications
ISBN: 0486829669
Category: Mathematics
Page: 224
View: 712
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The standard text on the subject for many years, this introductory treatment covers classical linear groups, topological groups, manifolds, analytic groups, differential calculus of Cartan, and compact Lie groups and their representations. 1946 edition.

Operators and Representation Theory

Canonical Models for Algebras of Operators Arising in Quantum Mechanics
Author: Palle E.T. Jorgensen
Publisher: Courier Dover Publications
ISBN: 0486822575
Category: Science
Page: 304
View: 7919
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Three-part treatment covers background material on definitions, terminology, operators in Hilbert space domains of representations, operators in the enveloping algebra, spectral theory; and covariant representation and connections. 2017 edition.

Abstract Lie Algebras


Author: David J Winter
Publisher: Courier Corporation
ISBN: 0486783464
Category: Mathematics
Page: 160
View: 8742
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Solid but concise, this account of Lie algebra emphasizes the theory's simplicity and offers new approaches to major theorems. Author David J. Winter, a Professor of Mathematics at the University of Michigan, also presents a general, extensive treatment of Cartan and related Lie subalgebras over arbitrary fields. Preliminary material covers modules and nonassociate algebras, followed by a compact, self-contained development of the theory of Lie algebras of characteristic 0. Topics include solvable and nilpotent Lie algebras, Cartan subalgebras, and Levi's radical splitting theorem and the complete reducibility of representations of semisimple Lie algebras. Additional subjects include the isomorphism theorem for semisimple Lie algebras and their irreducible modules, automorphism of Lie algebras, and the conjugacy of Cartan subalgebras and Borel subalgebras. An extensive theory of Cartan and related subalgebras of Lie algebras over arbitrary fields is developed in the final chapter, and an appendix offers background on the Zariski topology.

Semi-Simple Lie Algebras and Their Representations


Author: Robert N. Cahn
Publisher: Courier Corporation
ISBN: 0486150313
Category: Mathematics
Page: 176
View: 4816
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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. 1984 edition.

Lehrbuch der Algebra

Mit lebendigen Beispielen, ausführlichen Erläuterungen und zahlreichen Bildern
Author: Gerd Fischer
Publisher: Springer-Verlag
ISBN: 3834894559
Category: Mathematics
Page: 404
View: 3181
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Dieses ausführlich geschriebene Lehrbuch eignet sich als Begleittext zu einer einführenden Vorlesung über Algebra. Die Themenkreise sind Gruppen als Methode zum Studium von Symmetrien verschiedener Art, Ringe mit besonderem Gewicht auf Fragen der Teilbarkeit und schließlich als Schwerpunkt Körpererweiterungen und Galois-Theorie als Grundlage für die Lösung klassischer Probleme zur Berechnung der Nullstellen von Polynomen und zur Möglichkeit geometrischer Konstruktionen.

Lie Groups for Pedestrians


Author: Harry J. Lipkin
Publisher: Courier Corporation
ISBN: 9780486421858
Category: Science
Page: 182
View: 2438
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This book shows how the well-known methods of angular momentum algebra can be extended to treat other Lie groups. Chapters cover isospin; the three-dimensional harmonic oscillator; algebras of operators that change the number of particles; permutations, bookkeeping, and Young diagrams; and more. 1966 edition.

Gradings on Simple Lie Algebras


Author: Alberto Elduque,Mikhail Kochetov
Publisher: American Mathematical Soc.
ISBN: 0821898469
Category: Mathematics
Page: 336
View: 5631
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Gradings are ubiquitous in the theory of Lie algebras, from the root space decomposition of a complex semisimple Lie algebra relative to a Cartan subalgebra to the beautiful Dempwolff decomposition of $E_8$ as a direct sum of thirty-one Cartan subalgebras. This monograph is a self-contained exposition of the classification of gradings by arbitrary groups on classical simple Lie algebras over algebraically closed fields of characteristic not equal to 2 as well as on some nonclassical simple Lie algebras in positive characteristic. Other important algebras also enter the stage: matrix algebras, the octonions, and the Albert algebra. Most of the presented results are recent and have not yet appeared in book form. This work can be used as a textbook for graduate students or as a reference for researchers in Lie theory and neighboring areas.

Thinking in Problems

How Mathematicians Find Creative Solutions
Author: Alexander A. Roytvarf
Publisher: Springer Science & Business Media
ISBN: 0817684069
Category: Mathematics
Page: 405
View: 2437
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This concise, self-contained textbook gives an in-depth look at problem-solving from a mathematician’s point-of-view. Each chapter builds off the previous one, while introducing a variety of methods that could be used when approaching any given problem. Creative thinking is the key to solving mathematical problems, and this book outlines the tools necessary to improve the reader’s technique. The text is divided into twelve chapters, each providing corresponding hints, explanations, and finalization of solutions for the problems in the given chapter. For the reader’s convenience, each exercise is marked with the required background level. This book implements a variety of strategies that can be used to solve mathematical problems in fields such as analysis, calculus, linear and multilinear algebra and combinatorics. It includes applications to mathematical physics, geometry, and other branches of mathematics. Also provided within the text are real-life problems in engineering and technology. Thinking in Problems is intended for advanced undergraduate and graduate students in the classroom or as a self-study guide. Prerequisites include linear algebra and analysis.

The Book of Involutions


Author: Max-Albert Knus
Publisher: American Mathematical Soc.
ISBN: 9780821873212
Category: Mathematics
Page: 593
View: 5743
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This monograph is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. It provides the algebra-theoretic foundations for much of the recent work on linear algebraic groups over arbitrary fields. Involutions are viewed as twisted forms of (hermitian) quadrics, leading to new developments on the model of the algebraic theory of quadratic forms. In addition to classical groups, phenomena related to triality are also discussed, as well as groups of type $F_4$ or $G_2$ arising from exceptional Jordan or composition algebras. Several results and notions appear here for the first time, notably the discriminant algebra of an algebra with unitary involution and the algebra-theoretic counterpart to linear groups of type $D_4$. This volume also contains a Bibliography and Index. Features: original material not in print elsewhere a comprehensive discussion of algebra-theoretic and group-theoretic aspects extensive notes that give historical perspective and a survey on the literature rational methods that allow possible generalization to more general base rings

Galoissche Theorie


Author: Emil Artin
Publisher: N.A
ISBN: N.A
Category: Galois theory
Page: 86
View: 1713
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Algebra

Unter Benutzung von Vorlesungen von E. Artin und E. Noether
Author: Bartel L. van der Waerden
Publisher: Springer-Verlag
ISBN: 3662216000
Category: Mathematics
Page: 275
View: 7448
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An Introduction to Linear Algebra and Tensors


Author: Maks A?zikovich Akivis,Vladislav Viktorovich Gol?dberg
Publisher: Courier Corporation
ISBN: 9780486635453
Category: Mathematics
Page: 167
View: 1639
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Eminently readable and completely elementary, this treatment begins with linear spaces and ends with analytic geometry. Additional topics include multilinear forms, tensors, linear transformation, eigenvectors and eigenvalues, matrix polynomials, and more. More than 250 carefully chosen problems appear throughout the book, most with hints and answers. 1972 edition.

Curvature in Mathematics and Physics


Author: Shlomo Sternberg
Publisher: Courier Corporation
ISBN: 0486292711
Category: Mathematics
Page: 416
View: 9328
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Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.

Basic Algebra I

Second Edition
Author: Nathan Jacobson
Publisher: Courier Corporation
ISBN: 0486135225
Category: Mathematics
Page: 528
View: 9752
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A classic text and standard reference for a generation, this volume covers all undergraduate algebra topics, including groups, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. 1985 edition.

Algebra

Aus dem Englischen übersetzt von Annette A’Campo
Author: Michael Artin
Publisher: Birkhäuser
ISBN: 9783764359386
Category: Mathematics
Page: 705
View: 3862
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Important though the general concepts and propositions may be with which the modem and industrious passion for axiomatizing and generalizing has presented us, in algebra perhaps more than anywhere else, nevertheless I am convinced that the special problems in all their complexity constitute the stock and core of mathematics, and that to master their difficulties requires on the whole the harder labor. HERMANN WEYL Die Arbeit an diesem Buch begann vor etwa zwanzig Jahren mit Aufzeichnungen zur Ergänzung meiner Algebravorlesungen. Ich wollte einige konkrete Themen, wie Symmetrie, lineare Gruppen und quadratische Zahlkörper, ausführlicher be­ handeln als dies im vorgesehenen Text der Fall war, und darüberhinaus wollte ich den Schwerpunkt in der Gruppentheorie von den Permutationsgruppen auf Matrixgruppen verlagern. Ein anderes ständig wiederkehrendes Thema, nämlich Gitter, sind spontan aufgetaucht. Ich hoffte, der konkrete Stoff könne das Interesse der Studenten wecken und gleichzeitig die Abstraktionen verständlicher machen, kurz gesagt, sie sollten weiter kommen, indem sie beides gleichzeitig lernten. Das bewährte sich gut. Es dauerte einige Zeit, bis ich entschieden hatte, welche Themen ich behandeln wollte, und allmählich verteilte ich mehr und mehr Aufzeichnungen und ging schließlich dazu über, die ganze Vorlesung mit diesem Skript zu bestrei­ ten. Auf diese Weise ist ein Buch entstanden, das, wie ich meine, etwas anders ist als die existierenden Bücher. Allerdings haben mir die Probleme, die ich damit hatte, die einzelnen Teile des Buches zu einem Ganzen zusammenzufügen, einige Kopfschmerzen bereitet; ich kann also nicht empfehlen, auf diese Art anzufangen, ein Buch zu schreiben.

Harmonic Analysis on Homogeneous Spaces


Author: Nolan R. Wallach
Publisher: Courier Dover Publications
ISBN: 0486816923
Category: Mathematics
Page: 384
View: 1976
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Requiring background in linear algebra and advanced calculus, this text covers representation theory of compact Lie groups with applications to topology, geometry, and analysis and non-compact semi-simple Lie groups. 1973 edition.

Group Theory and Its Application to Physical Problems


Author: Morton Hamermesh
Publisher: Courier Corporation
ISBN: 0486140393
Category: Science
Page: 544
View: 8650
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One of the best-written, most skillful expositions of group theory and its physical applications, directed primarily to advanced undergraduate and graduate students in physics, especially quantum physics. With problems.

Matrizen und Lie-Gruppen

Eine geometrische Einführung
Author: Wolfgang Kühnel
Publisher: Springer-Verlag
ISBN: 3834899054
Category: Mathematics
Page: 224
View: 7344
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Dies ist eine Einführung in die mathematische Theorie der Lie-Gruppen. Etwa die erste Hälfte des Buches handelt von Matrizengruppen. Abstrakte Konzepte (auch Mannigfaltigkeiten) werden erst in der zweiten Hälfte vorgestellt. Zur Motivation und zum besseren historischen Verständnis sind kurze Texte klassischer Autoren (wie Sophus Lie selbst) mit eingeflochten. Außerdem gibt es zur Anschaulichkeit ein eigenes Kapitel, das ausschließlich von diversen geometrischen Transformationsgruppen handelt. Dabei wird konkret auf die klassischen Geometrien eingegangen. Als Vorkenntnisse werden nur die üblichen Studieninhalte des ersten Jahres im Mathematik- oder Physik-Studium vorausgesetzt, soweit sie die Analysis und die Lineare Algebra betreffen. Das Buch beginnt damit auf sehr elementarem Niveau. Alles andere wird nicht nur eingeführt, sondern alle Sätze werden auch bewiesen. Auf Verständlichkeit wird großen Wert gelegt. Daher eignet sich das Buch insbesondere als Begleittext zu Lehrveranstaltungen (auch Proseminaren) in den Bachelor-Studiengängen, aber auch im Lehramtsstudium und zum Selbststudium. Das Buch enthält zahlreiche Übungsaufgaben mit Lösungshinweisen oder vollständiger Lösung.