
Lie Groups, Lie Algebras, and Representations: v. 222: An Elementary Introduction (Graduate Texts in Mathematics) (Hardback)
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Dispatched in 4 business days When will my order arrive?  DescriptionLie groups, Lie algebras, and representation theory are the main focus of this text. In order to keep the prerequisites to a minimum, the author restricts attention to matrix Lie groups and Lie algebras. This approach keeps the discussion concrete, allows the reader to get to the heart of the subject quickly, and covers all of the most interesting examples. The book also introduces the oftenintimidating machinery of roots and the Weyl group in a gradual way, using examples and representation theory as motivation. The text is divided into two parts. The first covers Lie groups and Lie algebras and the relationship between them, along with basic representation theory. The second part covers the theory of semisimple Lie groups and Lie algebras, beginning with a detailed analysis of the representations of SU(3). The author illustrates the general theory with numerous images pertaining to Lie algebras of rank two and rank three, including images of root systems, lattices of dominant integral weights, and weight diagrams. This book is sure to become a standard textbook for graduate students in mathematics and physics with little or no prior exposure to Lie theory. Brian Hall is an Associate Professor of Mathematics at the University of Notre Dame.
 Publisher: SpringerVerlag New York Inc.
 Published: 01 December 2004
 Format: Hardback 368 pages
 See: Full bibliographic data
 Categories: Teaching Resources & Education  Mathematics  Algebra  Groups & Group Theory
 ISBN 13: 9780387401225 ISBN 10: 0387401229
 Sales rank: 457,760
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Full bibliographic data for Lie Groups, Lie Algebras, and Representations: v. 222
 Title
 Lie Groups, Lie Algebras, and Representations: v. 222
 Subtitle
 An Elementary Introduction
 Authors and contributors
 Physical properties
 Format: Hardback
Number of pages: 368
Width: 157 mm
Height: 236 mm
Thickness: 23 mm
Weight: 499 g  Language
 English
 ISBN
 ISBN 13: 9780387401225
ISBN 10: 0387401229  Classifications
BIC E4L: MAT
Nielsen BookScan Product Class 3: S7.8
B&T Book Type: NF
LC subject heading:
B&T Modifier: Region of Publication: 01
B&T Merchandise Category: SCI
B&T General Subject: 710
B&T Modifier: Academic Level: 02
Ingram Subject Code: MA
LC subject heading:
BIC subject category V2: PBF
LC subject heading:
WarengruppenSystematik des deutschen Buchhandels: 16240
BISAC V2.8: MAT002000, MAT014000, MAT019000
LC subject heading:
BISAC V2.8: MAT002050
LC subject heading: ,
BISAC V2.8: EDU000000
LC subject heading:
DC22: 512.55, 512/.55
LC subject heading: , ,
DC22: 512.482
LC classification: QA387
LC subject heading: ,
Libri: GRUP2054, LIES5000, P0041510
LC classification: QA387 .H34 2003, QA252.3, QA1939, QC5.53, QA150272, QA174183
Thema V1.0: JN, PBF Edition statement
 1st ed. 2003. Corr. 2nd printing 2004
 Illustrations note
 biography
 Publisher
 SpringerVerlag New York Inc.
 Imprint name
 SpringerVerlag New York Inc.
 Publication date
 01 December 2004
 Publication City/Country
 New York, NY
 Table of 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 BakerCampbellHausdorff Formula 3.1 The BakerCampbellHausdorff Formula for the Heisenberg Group 3.2 The General BakerCampbellHausdorff Formula 3.3 The Derivative of the Exponential Mapping 3.4 Proof of the BakerCampbellHausdorff Formula 3.5 The Series Form of the BakerCampbellHausdorff 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