Buch, Englisch, 172 Seiten, Format (B × H): 156 mm x 237 mm, Gewicht: 280 g
Reihe: Universitext
The Geometry of Finite Reflection Groups
Buch, Englisch, 172 Seiten, Format (B × H): 156 mm x 237 mm, Gewicht: 280 g
Reihe: Universitext
ISBN: 978-0-387-79065-7
Verlag: Springer
This graduate/advanced undergraduate textbook contains a systematic and elementary treatment 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. Key features include: many important concepts in the proofs are illustrated in simple drawings, which give easy access to the theory; a large number of exercises at various levels of difficulty; some Euclidean geometry is included along with the theory of convex polyhedra; no prerequisites are necessary beyond the basic concepts of linear algebra and group theory; and a good index and bibliography The exposition is directed at advanced undergraduates and first-year graduate students.
Zielgruppe
Graduate
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
- Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
- Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
- Mathematik | Informatik Mathematik Algebra Homologische Algebra
- Mathematik | Informatik Mathematik Geometrie Euklidische Geometrie
- Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
- Mathematik | Informatik Mathematik Operations Research Graphentheorie
Weitere Infos & Material
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.
