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Naive Lie theory
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The aim of this book is to carry it out—developing the central concepts and results of Lie theory by the simplest possible methods, mainly from single-variable calculus and linear algebra. Familiarity with elementary group theory is also desirable, but the author provides a crash course on the basics of group theory in Sections 2.1 and 2.2.
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Undergraduate Texts in Mathematics
Editors
S. Axler
K.A. Ribet
Undergraduate Texts in Mathematics
Abbott: Understanding Analysis.
Anglin: Mathematics: A Concise History and
Philosophy.
Readings in Mathematics.
Anglin/Lambek: The Heritage of Thales.
Readings in Mathematics.
Apostol: Introduction to Analytic Number Theory.
Second edition.
Armstrong: Basic Topology.
Armstrong: Groups and Symmetry.
Axler: Linear Algebra Done Right. Second edition.
Beardon: Limits: A New Approach to Real
Analysis.
Bak/Newman: Complex Analysis. Second edition.
Banchoff/Wermer: Linear Algebra Through
Geometry. Second edition.
Beck/Robins: Computing the Continuous
Discretely
Berberian: A First Course in Real Analysis.
Bix: Conics and Cubics: A Concrete Introduction to
Algebraic Curves. Second edition.
Br
`
emaud: An Introduction to Probabilistic
Modeling.
Bressoud: Factorization and Primality Testing.
Bressoud: Second Year Calculus.
Readings in Mathematics.
Brickman: Mathematical Introduction to Linear
Programming and Game Theory.
Browder: Mathematical Analysis: An Introduction.
Buchmann: Introduction to Cryptography. Second
Edition.
Buskes/van Rooij: Topological Spaces: From
Distance to Neighborhood.
Callahan: The Geometry of Spacetime: An
Introduction to Special and General Relavitity.
Carter/van Brunt: The Lebesgue– Stieltjes
Integral: A Practical Introduction.
Cederberg: A Course in Modern Geometries.
Second edition.
Chambert-Loir: A Field Guide to Algebra
Childs: A Concrete Introduction to Higher Algebra.
Second edition.
Chung/AitSahlia: Elementary Probability Theory:
With Stochastic Processes and an Introduction to
Mathematical Finance. Fourth edition.
Cox/Little/O’Shea: Ideals, Varieties, and
Algorithms. Second edition.
Croom: Basic Concepts of Algebraic Topology.
Cull/Flahive/Robson: Difference Equations. From
Rabbits to Chaos
Curtis: Linear Algebra: An Introductory Approach.
Fourth edition.
Daepp/Gorkin: Reading, Writing, and Proving:
A Closer Look at Mathematics.
Devlin: The Joy of Sets: Fundamentals
of-Contemporary Set Theory. Second edition.
Dixmier: General Topology.
Driver: Why Math?
Ebbinghaus/Flum/Thomas: Mathematical Logic.
Second edition.
Edgar: Measure, Topology, and Fractal Geometry.
Second edition.
Elaydi: An Introduction to Difference Equations.
Third edition.
Erd
˜
os/Sur
´
anyi: Topics in the Theory of Numbers.
Estep: Practical Analysis on One Variable.
Exner: An Accompaniment to Higher Mathematics.
Exner: Inside Calculus.
Fine/Rosenberger: The Fundamental Theory
of Algebra.
Fischer: Intermediate Real Analysis.
Flanigan/Kazdan: Calculus Two: Linear and
Nonlinear Functions. Second edition.
Fleming: Functions of Several Variables. Second
edition.
Foulds: Combinatorial Optimization for
Undergraduates.
Foulds: Optimization Techniques: An Introduction.
Franklin: Methods of Mathematical
Economics.
Frazier: An Introduction to Wavelets Through
Linear Algebra.
Gamelin: Complex Analysis.
Ghorpade/Limaye: A Course in Calculus and Real
Analysis
Gordon: Discrete Probability.
Hairer/Wanner: Analysis by Its History.
Readings in Mathematics.
Halmos: Finite-Dimensional Vector Spaces.
Second edition.
Halmos: Naive Set Theory.
H
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ammerlin/Hoffmann: Numerical Mathematics.
Readings in Mathematics.
Harris/Hirst/Mossinghoff: Combinatorics and
Graph Theory.
Hartshorne: Geometry: Euclid and Beyond.
Hijab: Introduction to Calculus and Classical
Analysis. Second edition.
Hilton/Holton/Pedersen: Mathematical
Reflections: In a Room with Many Mirrors.
Hilton/Holton/Pedersen: Mathematical Vistas:
From a Room with Many Windows.
Iooss/Joseph: Elementary Stability and Bifurcation
Theory. Second Edition.
(continued after index)
John Stillwell
Naive Lie Theory
123
John Stillwell
Department of Mathematics
University of San Francisco
San Francisco, CA 94117
USA
stillwell@usfca.edu
Editorial Board
S. Axler K.A. Ribet
Mathematics Department Department of Mathematics
San Francisco State University University of California
San Francisco, CA 94132 at Berkeley
USA Berkeley, CA 94720
axler@sfsu.edu USA
ribet@math.berkeley.edu
ISBN: 978-0-387-78214-0 e-ISBN: 978-0-387-78215-7
DOI: 10.1007/978-0-387-78214-0
Library of Congress Control Number: 2008927921
Mathematics Subject Classification (2000): 22Exx:22E60
c
2008 Springer Science+Business Media, LLC
All rights reserved. This work may not be translated or copied in whole or in part without the written
permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York,
NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use
in connection with any form of information storage and retrieval, electronic adaptation, computer
software, or by similar or dissimilar methodology now known or hereafter developed is forbidden.
The use in this publication of trade names, trademarks, service marks, and similar terms, even if they
are not identified as such, is not to be taken as an expression of opinion as to whether or not they are
subject to proprietary rights.
Printed on acid-free paper
987654321
springer.com
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