Mirrors and Reflections
The Geometry of Finite Reflection Groups
Seiten
2009
|
2010 ed.
Springer-Verlag New York Inc.
978-0-387-79065-7 (ISBN)
Springer-Verlag New York Inc.
978-0-387-79065-7 (ISBN)
"Mirrors and Reflections" presents a systematic and elementary introduction to the properties of finite groups generated by reflections. The approach is based on fundamental geometric considerations in Coxeter complexes, and emphasizes the intuitive geometric aspects of the theory of reflection groups. The exposition is directed at advanced undergraduates and first-year graduate students, and features a large number of exercises at various levels of difficulty.
Geometric Background.- Affine Euclidean Space .- Isometries of .- Hyperplane Arrangements.- Polyhedral Cones.- Mirrors, Reflections, Roots.- Mirrors and Reflections.- Systems of Mirrors.- Dihedral Groups.- Root Systems.- Root Systems An?1, BCn, Dn.- Coxeter Complexes.- Chambers.- Generation.- Coxeter Complex.- Residues.- Generalized Permutahedra.- Classification.- Generators and Relations.- Classification of Finite Reflection Groups.- Construction of Root Systems.- Orders of Reflection Groups.- Three-Dimensional Reflection Groups.- Reflection Groups in Three Dimensions.- Icosahedron.
| Reihe/Serie | Universitext |
|---|---|
| Zusatzinfo | 74 Illustrations, black and white; XII, 172 p. 74 illus. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 0-387-79065-9 / 0387790659 |
| ISBN-13 | 978-0-387-79065-7 / 9780387790657 |
| Zustand | Neuware |
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