Lie groups and lie algebras

Preface ix
1. Notational Conventions and Other Preliminaries 1
2. Analytic Functions 23
3. Analytic Manifolds 45
4. Lie Groups 65
5. Lie Groups: The Theorems of Cartan and Lie 85
6. Lie Algebras: Theorems of Engel, Lie and Cartan 105
7. Lie Algebras: Structure Theory 125
References 143
Index 145
The Alphabet in Roman and Gothic Scripts 147

This is a textbook 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 found in the first of the Bourbaki volumes on the subject. Some proofs here are new.