This is a text book meant to be used at the advanced undergraduate or graduate level. It is an introduction to the theory of Lie groups and Lie algebras. The book treats real and p-adic groups in a unified manner. The first chapter outlines preliminary material that is used in the rest of the book. The second chapter is on analytic functions and is of an elementary nature; this material is included to cater to students who may not be familiar with p-adic fields. The third chapter introduces analytic manifolds and contains standard material; the only notable feature being that it covers both real and p-adic analytic manifolds. Chapters 4 and 5 are on Lie groups. All the standard results on Lie groups are proved here. Some of the proofs are different from those in the earlier literature. The last two chapters are on Lie algebras and cover their structure theory as to be found in the first of the Bourbaki volumes on the subject. Some proofs here are new.
1. Notational Conventions and Other Preliminaries
2. Analytic Functions
3. Analytic Manifolds
4. Lie Groups
5. Lie Groups: The Theorems of Cartan and Lie
6. Lie Algebras: Theorems of Engel, Lie and Cartan
7. Lie Algebras: Structure Theory
References
Index
The Alphabet in Roman and Gothic Scripts