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Lie groups, lie algebras, and representations : an elementary introduction

Author: Brian C Hall
Publisher: New York, NY : Springer, 2004.
Series: Graduate texts in mathematics, 222.
Edition/Format:   Print book : English : Corr. 2. printView all editions and formats
Summary:

Intended for graduate students in mathematics and physics, this book provides an introduction to Lie groups, Lie algebras, and representation theory.

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Genre/Form: Lehrbuch
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Brian C Hall
ISBN: 0387401229 9780387401225 9780387215549 0387215549 9781441923134 1441923136
OCLC Number: 249922892
Notes: Literaturverz. S. [345] - 346.
Description: XIV, 351 Seiten : Illustrationen, Diagramme.
Contents: Preface Part I General Theory 1 Matrix Lie Groups 1.1 Definition of a Matrix Lie Group 1.2 Examples of Matrix Lie Groups 1.3 Compactness 1.4 Connectedness 1.5 Simple Connectedness 1.6 Homomorphisms and Isomorphisms 1.7 (Optional) The Polar Decomposition for $ {SL}(n; {R})$ and $ {SL}(n; {C})$ 1.8 Lie Groups 1.9 Exercises 2 Lie Algebras and the Exponential Mapping 2.1 The Matrix Exponential 2.2 Computing the Exponential of a Matrix 2.3 The Matrix Logarithm 2.4 Further Properties of the Matrix Exponential 2.5 The Lie Algebra of a Matrix Lie Group 2.6 Properties of the Lie Algebra 2.7 The Exponential Mapping 2.8 Lie Algebras 2.9 The Complexification of a Real Lie Algebra 2.10 Exercises 3 The Baker--Campbell--Hausdorff Formula 3.1 The Baker--Campbell--Hausdorff Formula for the Heisenberg Group 3.2 The General Baker--Campbell--Hausdorff Formula 3.3 The Derivative of the Exponential Mapping 3.4 Proof of the Baker--Campbell--Hausdorff Formula 3.5 The Series Form of the Baker--Campbell--Hausdorff Formula 3.6 Lie Algebra Versus Lie Group Homomorphisms 3.7 Covering Groups 3.8 Subgroups and Subalgebras 3.9 Exercises 4 Basic Representation Theory 4.1 Representations 4.2 Why Study Representations? 4.3 Examples of Representations 4.4 The Irreducible Representations of $ {su}(2)$ 4.5 Direct Sums of Representations 4.6 Tensor Products of Representations 4.7 Dual Representations 4.8 Schur's Lemma 4.9 Group Versus Lie Algebra Representations 4.10 Complete Reducibility 4.11 Exercises Part II Semisimple Theory 5 The Representations of $ {SU}(3)$ 5.1 Introduction 5.2 Weights and Roots 5.3 The Theorem of the Highest Weight 5.4 Proof of the Theorem 5.5 An Example: Highest Weight $( 1,1) $ 5.6 The Weyl Group 5.7 Weight Diagrams 5.8 Exercises 6 Semisimple Lie Algebras 6.1 Complete Reducibility and Semisimple Lie Algebras 6.2 Examples of Reductive and
Series Title: Graduate texts in mathematics, 222.
Responsibility: Brian C. Hall.

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From the reviews: "This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... . It is clearly written ... . A reader Read more...

 
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