Lie Groups, Lie Algebras, and Representations: An Elementary Introduction (Graduate Texts in Mathematics, 222) - First edition

EAN (ISBN-13): 9780387401225
ISBN (ISBN-10): 0387401229
Hardcover
Paperback
Publishing year: 2004
Publisher: Springer
351 Pages
Weight: 0,690 kg
Language: eng/Englisch

Book in our database since 2007-06-12T04:47:51-04:00 (New York)
Detail page last modified on 2024-02-17T00:45:51-05:00 (New York)
ISBN/EAN: 0387401229

ISBN - alternate spelling:
0-387-40122-9, 978-0-387-40122-5
Alternate spelling and related search-keywords:
Book author: hall, dynkin, weyl, may brian, rank, lie
Book title: introduction lie groups, elementary algebra, 222, representation, group, graduate text mathematics, the graduate, graduate texts mathematics, lie groups lie algebras and representations

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Information from Publisher

Author: Brian Hall
Title: Graduate Texts in Mathematics; Lie Groups, Lie Algebras, and Representations - An Elementary Introduction
Publisher: Springer; Springer US
354 Pages
Publishing year: 2004-08-27
New York; NY; US
Weight: 1,550 kg
Language: English
53,45 € (DE)
54,95 € (AT)
77,58 CHF (CH)
Not available, publisher indicates OP

BB; Book; Hardcover, Softcover / Mathematik/Arithmetik, Algebra; Algebra; linear algebra; Matrix; Eigenvalue; Representation theory; Vector space; algebra; Eigenvector; Lie algebra; Permutation; Mathematics and Statistics; B; Algebra; Group Theory and Generalizations; Topological Groups, Lie Groups; Mathematical Methods in Physics; Gruppen und Gruppentheorie; Gruppen und Gruppentheorie; Mathematische Physik; BC; EA; BB

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
This book provides an introduction to Lie groups, Lie algebras, and representation theory, aimed at graduate studnets in mathematics and physics.