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Series in Pure Mathematics - Vol. 13
INTRODUCTION TO COMPACT LIE GROUPS
by Howard D Fegan (University of New Mexico, USA)
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.
Contents:
- Calculus on Manifolds
- Groups and Lie Groups
- One-Parameter
Subgroups and the Exponential Map
- The Campbell-Baker-Hausdorff Formula
- The Adjoint Representation
- Maximal Tori
- Representation Theory
- Roots and Weights
- Weyl's Formulae
- Differential Operators on Compact Lie Groups
- The Riemannian Geometry of a Compact Lie Group
- The Trace of the Heat Kernel
Readership: Graduate students in mathematics, mathematicians and physicists.
| 148pp |
Pub. date: Jul 1991 |
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