Preface * Prerequisites by chapter * Standard Notation * I. Lie Algebras and Lie Groups * II. Complex Semisimple Lie Algebras * III. Universal Enveloping Algebra * IV. Compact Lie Groups * V. Finite-Dimensional Representations * VI. Structure Theory of Semisimple Groups * VII. Advanced Structure Theory * VIII. Integration * IX. Induced Representations and Branching Theorems * X. Prehomogeneous Vector Spaces * Appendices * Hints for Solutions of Problems * Notes * References * Index of Notation * Index

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.