patience please...


*      Contents (below)

*      Preface (PDF )

*      Section 1.1. Vector fields and
one parameter groups (PDF  223KB)

*      From section 2.5.  The Lie correspondence (PDF)

*      Review by A. Knapp,
American Mathematical Monthly (PDF)

*      Review by P. Trapa,
AMS Bulletin (PDF)

*      Corrections and comments (Aug 2004, PDF)












1  The exponential map

1.1  Vector fields and one-parameter groups of linear transformations

1.2  Ad, ad, and dexp

1.3  The Campbell-Baker-Hausdorff Series

2  Lie theory

2.1  Linear groups: definitions and examples

2.2  The Lie algebra of a linear group

2.3  Coordinates on a linear group

2.4  Connectedness

2.5  The Lie correspondence

2.6  Homomorphisms and coverings of linear groups

2.7  Closed subgroups

3  The classical groups

3.1  The classical groups: definitions, connectedness

3.2  Cartan subgroups

3.3  Roots, weights, reflections

3.4  Fundamental groups of the classical groups




4  Manifolds, homogeneous spaces, Lie groups

4.1  Manifolds

4.2  Homogeneous spaces

4.3  General Lie groups

5  Integration

5.1  Integration on manifolds

5.2  Integration on linear groups and their homogeneous spaces

5.3  Weyl's Integration Formula for U(n)

6  Representations

6.1  Representations: definitions

6.2  Schur's Lemma and its consequences; Peter-Weyl Theorem

6.3  Characters

6.4  Weyl's Character Formula for U(n)

6.5  Representations of Lie algebras

6.6  The Borel-Weil Theorem for GL(n, C)

6.7 Representations of the classical groups

Appendix: The Inverse Function Theorem




A Mathematica implementation of Example 1.1.4

by Tony Thrall