Chapter 1 introduces some of the terminology and notation used later and indicates prerequisites. Chapter 2 gives a reasonably thorough account of all finite subgroups of the orthogonal groups in two and three dimensions. The presentation is somewhat less formal than in succeeding chapters. For instance, the existence of the icosahedron is accepted as an empirical fact, and no formal proof of existence is included. Throughout most of Chapter 2 we do not distinguish between groups that are geo metrically indistinguishable, that is, conjugate in the orthogonal group. Very little of the material in Chapter 2 is actually required for the sub sequent chapters, but it serves two important purposes: It aids in the development of geometrical insight, and it serves as a source of illustrative examples. There is a discussion offundamental regions in Chapter 3. Chapter 4 provides a correspondence between fundamental reflections and funda mental regions via a discussion of root systems. The actual classification and construction of finite reflection groups takes place in Chapter 5. where we have in part followed the methods of E. Witt and B. L. van der Waerden. Generators and relations for finite reflection groups are discussed in Chapter 6. There are historical remarks and suggestions for further reading in a Post lude.
Product Identifiers
Publisher
Springer-Verlag New York Inc.
ISBN-13
9781441930729
eBay Product ID (ePID)
178113362
Product Key Features
Author
C.T. Benson, L.C. Grove
Publication Name
Finite Reflection Groups
Format
Paperback
Language
English
Subject
Mathematics
Publication Year
2010
Type
Textbook
Number of Pages
136 Pages
Dimensions
Item Height
254mm
Item Width
178mm
Volume
99
Item Weight
600g
Additional Product Features
Title_Author
C.T. Benson, L.C. Grove
Series Title
Graduate Texts in Mathematics
Country/Region of Manufacture
United States
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