Bibliographical references (pp783-798)

Preface to the Second Edition; Preface to the First Edition; List of Figures; Prerequisites by Chapter; Standard Notation; Introduction: Closed Linear Groups; Lie Algebras and Lie Groups; Complex Semisimple Lie Algebras; Universal Enveloping Algebra; Compact Lie Groups; Finite-Dimensional Representations; Structure Theory of Semisimple Groups; Advanced Structure Theory Integration; Induced Representations and Branching Theorems; Prehomogeneous Vector Spaces; Appendices; Hints for Solutions of Problems; Historical Notes; References; Index of Notation; Index

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 covered in this title 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