Mirrors and reflections: the geometry of finite reflection groups

'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. Many important concepts in the proofs are illustrated through simple drawings, which give easy access to the theory Includes numerous exercises at various levels of difficulty as well as an appendix with hints for solving many of the more difficult problems Provides an introduction to the necessary elements of Euclidean geometry and the theory of convex polyhedra Few prerequisites are necessary beyond linear algebra and the basic principles of group theory INDICE: Part I Geometric Background.- 1. Affine Euclidean Space ARn.- 2 Isometries of ARn .- 3 Hyperplane Arrangements.- 4 Polyhedral Cones.- 5 Mirrors and Reflections.- 6 Systems of Mirrors.- 7 Dihedral Groups.- 8 Root Systems.- 9 Root Systems Aní1, BCn, Dn.- 10 Chambers.- 11 Generation.- 12 Coxeter Complex.- 13 Residues.- 14 Generalized Permutahedra.- Part IV Classification.- 15 Generators and Relations.- 16 Classification of Finite Reflection Groups.- 17 Construction of Root Systems.- 18 Orders of Reflection Groups.- Part V Three-Dimensional Reflection Groups.- 19 Reflection Groups in Three Dimensions.- 20 Icosahedron.- Part VI Appendices.- References.- Index.

• ISBN: 978-0-387-79065-7
• Editorial: Springer
• Encuadernacion: Rústica
• Páginas: 172
• Fecha Publicación: 01/11/2009
• Nº Volúmenes: 1
• Idioma: Inglés