Introduction to Compact Lie Groups

Howard D Fegan

• Publisher: WSPC
• Year: 1991
• eBook ISBN: 9789813103467
• Topic: Biological Sciences
• Subtopic: Science General
• Index: Biological Sciences

There are two approaches to compact lie groups: by computation as matrices or theoretically as manifolds with a group structure. The great appeal of this book is the blending of these two approaches. The theoretical results are illustrated by computations and the theory provides a commentary on the computational work. Indeed, there are extensive computations of the structure and representation theory for the classical groups SU(n), SO(n) and Sp(n). A second exciting feature is that the differential geometry of a compact Lie group, both the classical curvature studies and the more recent heat equation methods, are treated. A large number of formulas for the connection and curvature are conveniently gathered together.

This book provides an excellent text for a first course in compact Lie groups.

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Table of contents

• Contents
• Preface
• Chapter 1 Calculus on Manifolds
• Chapter 2 Groups and Lie Groups
• Chapter 3 One-Parameter Subgroups and the Exponential Map
• Chapter 4 The Campbell-Baker-Hausdorff Formula
• Chapter 5 The Adjoint Representation
• Chapter 6 Maximal Tori
• Chapter 7 Representation Theory
• Chapter 8 Roots and Weights
• Chapter 9 Weyl's Formulae
• Chapter 10 Differential Operators on Compact Lie Groups
• Chapter 11 The Riemannian Geometry of a Compact Lie Group
• Chapter 12 The Trace of the Heat Kernel
• Appendix 1: The Tensor Product
• Appendix 2: Clifford Algebras and the Spin Groups
• Solutions and Hints for Selected Exercises
• Bibliography
• Index