Lie Groups Beyond an Introduction

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Springer Science & Business Media, Aug 21, 2002 - Mathematics - 812 pages
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From reviews of the first edition: "The important feature of the present book is that it starts from the beginning (with only a very modest knowledge assumed) and covers all important topics... The book is very carefully organized [and] ends with 20 pages of useful historic comments. Such a comprehensive and carefully written treatment of fundamentals of the theory will certainly be a basic reference and text book in the future." -- Newsletter of the EMS "This is a fundamental book and none, beginner or expert, could afford to ignore it. Some results are really difficult to be found in other monographs, while others are for the first time included in a book." -- Mathematica "Each chapter begins with an excellent summary of the content and ends with an exercise section... This is really an outstanding book, well written and beautifully produced. It is both a graduate text and a monograph, so it can be recommended to graduate students as well as to specialists." -- Publicationes Mathematicae Lie Groups Beyond an Introduction takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. A feature of the presentation is that it encourages the reader's comprehension of Lie group theory to evolve from beginner to expert: initial insights make use of actual matrices, while later insights come from such structural features as properties of root systems, or relationships among subgroups, or patterns among different subgroups. Topics include a description of all simply connected Lie groups in terms of semisimple Lie groups and semidirect products, the Cartan theory of complex semisimple Lie algebras, the Cartan-Weyl theory of the structure and representations of compact Lie groups and representations of complex semisimple Lie algebras, the classification of real semisimple Lie algebras, the structure theory of noncompact reductive Lie groups as it is now used in research, and integration on reductive groups. Many problems, tables, and bibliographical notes complete this comprehensive work, making the text suitable either for self-study or for courses in the second year of graduate study and beyond.
  

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Contents

XIII
23
XIV
24
XV
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XVI
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XVII
38
XVIII
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XIX
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XX
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LXXV
368
LXXVI
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LXXVII
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LXXVIII
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LXXIX
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LXXX
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LXXXI
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LXXXII
422

XXI
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XXII
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XXIV
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XXVII
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XXVIII
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XXIX
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XXX
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XXXI
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XXXIV
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XXXV
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XXXVI
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XXXVII
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XXXVIII
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XXXIX
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XL
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XLI
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XLV
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L
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LI
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LIII
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LIV
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LV
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LVI
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LVIII
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LIX
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LX
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LXI
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LXIII
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LXIV
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LXV
290
LXVI
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LXVII
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LXIX
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LXX
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LXXI
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LXXII
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LXXIII
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LXXIV
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LXXXIII
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LXXXIV
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LXXXV
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LXXXVII
458
LXXXVIII
460
LXXXIX
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XC
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XCI
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514
XCV
523
XCVI
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XCIX
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C
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CI
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CIII
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CIV
568
CV
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CVI
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CIX
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CXI
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CXXI
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CXXX
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CXXXII
719
CXXXIII
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CXXXIV
784
CXXXV
799
CXXXVI
805
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