Gilmore, Robert, 1941-
- Publication date:
- Cambridge : Cambridge University Press, 2008.
- xi, 319 p. : ill ; 26 cm.
Includes bibliographical references (p. 309-312) and index.
- Lie groups
- Matrix groups
- Lie algebras
- Matrix algebras
- Operator algebras
- Structure theory for Lie algebras
- Structure theory for simple Lie algebras
- Root spaces and Dynkin diagrams
- Real forms
- Riemannian symmetric spaces
- Hydrogenic atoms
- Maxwell's equations
- Lie groups and differential equations.
"Describing many of the most important aspects of Lie group theory, this book presents the subject in a hands-on way. Rather than concentrating on theorems and proofs, the book shows the relationship of Lie groups to many branches of mathematics and physics and illustrates these with concrete computations. Many examples of Lie groups and Lie algebras are given throughout the text, with applications of the material to physical sciences and applied mathematics.
The relation between Lie group theory and algorithms for solving ordinary differential equations is presented and shown to be analogous to the relation between Galois groups and algorithms for solving polynomial equations, other chapters are devoted to differential geometry, relativity, electrodynamics, and the hydrogen atom." "Problems are given at the end of each chapter so readers can monitor their understanding of the materials. This is a fascinating introduction to Lie groups for graduate and undergraduate students in physics, mathematics, and electrical engineering, as well as researchers in these fields."--BOOK JACKET.