
Lie Groups
A Problem-Oriented Introduction Via Matrix Groups
Harriet Pollatsek(Author)
American Mathematical Society (Publisher)
Published on 15. November 2009
Book
Paperback/Softback
177 pages
978-1-4704-7914-5 (ISBN)
Description
This textbook is a complete introduction to Lie groups for undergraduate students. The only prerequisites are multi-variable calculus and linear algebra. The emphasis is placed on the algebraic ideas, with just enough analysis to define the tangent space and the differential and to make sense of the exponential map. This textbook works on the principle that students learn best when they are actively engaged. To this end nearly 200 problems are included in the text, ranging from the routine to the challenging level. Every chapter has a section called ""Putting the pieces together"" in which all definitions and results are collected for reference and further reading is suggested.
Reviews / Votes
The strength of the Pollatsek book lies in its many exercises and its many opportunities for students to explore ideas that arise during the development of Lie theory....If you want to teach a course that introduces students to the richness of mathematics within the context of Lie theory and leads them to explore mathematical possibilities that arise in this interplay of algebra and calculus I recommend Pollatsek.""- The UMAP JournalMore details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
ISBN-13
978-1-4704-7914-5 (9781470479145)
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Schweitzer Classification
Content
Chapter 1. Symmetries of vector spaces
Chapter 2. Complex numbers, quaternions and geometry
Chapter 3. Linearization
Chapter 4. One-parameter subgroups and the exponential map
Chapter 5. Lie algebras
Chapter 6. Matrix groups over other fields
Appendix I. Linear algebra facts
Appendix II. Paper assignment used at Mount Holyoke College
Appendix III. Opportunities for further study
Chapter 2. Complex numbers, quaternions and geometry
Chapter 3. Linearization
Chapter 4. One-parameter subgroups and the exponential map
Chapter 5. Lie algebras
Chapter 6. Matrix groups over other fields
Appendix I. Linear algebra facts
Appendix II. Paper assignment used at Mount Holyoke College
Appendix III. Opportunities for further study