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

EAN (ISBN-13): 9780387401225
ISBN (ISBN-10): 0387401229
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 2004
Herausgeber: Springer
351 Seiten
Gewicht: 0,690 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 2007-06-12T10:47:51+02:00 (Berlin)
Detailseite zuletzt geändert am 2024-02-17T06:45:51+01:00 (Berlin)
ISBN/EAN: 9780387401225

ISBN - alternative Schreibweisen:
0-387-40122-9, 978-0-387-40122-5
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: hall, dynkin, weyl, may brian, rank, lie
Titel des Buches: 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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Daten vom Verlag:

Autor/in: Brian Hall
Titel: Graduate Texts in Mathematics; Lie Groups, Lie Algebras, and Representations - An Elementary Introduction
Verlag: Springer; Springer US
354 Seiten
Erscheinungsjahr: 2004-08-27
New York; NY; US
Gewicht: 1,550 kg
Sprache: Englisch
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.