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＜電子ブック＞
Mirrors and Reflections : The Geometry of Finite Reflection Groups / by Alexandre V. Borovik, Anna Borovik
(Universitext. ISSN:21916675)

版	1st ed. 2010.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2010
本文言語	英語
大きさ	XII, 172 p. 74 illus : online resource
著者標目	*Borovik, Alexandre V author Borovik, Anna author SpringerLink (Online service)
件　名	LCSH:Geometry LCSH:Algebra LCSH:Group theory LCSH:Topological groups LCSH:Lie groups LCSH:Algebras, Linear LCSH:Mathematical physics FREE:Geometry FREE:Algebra FREE:Group Theory and Generalizations FREE:Topological Groups and Lie Groups FREE:Linear Algebra FREE:Mathematical Methods in Physics
一般注記	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 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. Oftenconsidered 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 HTTP:URL=https://doi.org/10.1007/978-0-387-79066-4

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