# Lie Groups Beyond an Introduction

Part of the Progress in Mathematics book series (PM, volume 140)

Part of the Progress in Mathematics book series (PM, volume 140)

*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.

Algebra/Rings Group representation Group theory Groups & Generalizations Lie Groups Math Physics Mathematics Representation/Lie Group Vector space algebra

- DOI https://doi.org/10.1007/978-1-4757-2453-0
- Copyright Information Birkhäuser Boston 1996
- Publisher Name Birkhäuser, Boston, MA
- eBook Packages Springer Book Archive
- Print ISBN 978-1-4757-2455-4
- Online ISBN 978-1-4757-2453-0
- Series Print ISSN 0743-1643
- Series Online ISSN 2296-505X
- About this book