TY  - BOOK
AU  - Borovik,Alexandre V.
AU  - Borovik,Anna
ED  - SpringerLink (Online service)
TI  - Mirrors and Reflections
T2  - Universitext
SN  - 9780387790664
AV  - QA440-699 
U1  - 516 23
PY  - 2010///
CY  - New York, NY
PB  - Springer New York
KW  - Mathematics
KW  - Algebra
KW  - Group theory
KW  - Matrix theory
KW  - Topological groups
KW  - Lie groups
KW  - Geometry
KW  - Physics
KW  - Group Theory and Generalizations
KW  - Topological Groups, Lie Groups
KW  - Linear and Multilinear Algebras, Matrix Theory
KW  - Mathematical Methods in Physics
N1  - 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
N2  - Mirrors and Reflections presents an intuitive and elementary introduction to finite reflection groups. Starting with basic principles, this book provides a comprehensive classification of the various types of finite reflection groups and describes their underlying geometric properties. Unique to this text is its emphasis on the intuitive geometric aspects of the theory of reflection groups, making the subject more accessible to the novice. Primarily self-contained, necessary geometric concepts are introduced and explained. Principally designed for coursework, this book is saturated with exercises and examples of varying degrees of difficulty. An appendix offers hints for solving the most difficult problems. Wherever possible, concepts are presented with pictures and diagrams intentionally drawn for easy reproduction. Finite reflection groups is a topic of great interest to many pure and applied mathematicians. Often considered a cornerstone of modern algebra and geometry, an understanding of finite reflection groups is of great value to students of pure or applied mathematics. Requiring only a modest knowledge of linear algebra and group theory, this book is intended for teachers and students of mathematics at the advanced undergraduate and graduate levels
UR  - http://dx.doi.org/10.1007/978-0-387-79066-4
ER  -