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Mirrors and Reflections
The Geometry of Finite Reflection Groups
Taschenbuch von Alexandre V Borovik (u. a.)
Sprache: Englisch

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Beschreibung

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.

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.

Zusammenfassung
"Mirrors and Reflections" is 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. The exposition is directed at advanced undergraduates and first-year graduate students, and features a large number of exercises at various levels of difficulty.
Inhaltsverzeichnis
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.
Details
Medium: Taschenbuch
Seiten: 172
Inhalt: xii
172 S.
74 s/w Illustr.
172 p. 74 illus.
ISBN-13: 9780387790657
ISBN-10: 0387790659
Sprache: Englisch
Herstellernummer: 11560760
Einband: Kartoniert / Broschiert
Autor: Borovik, Alexandre V
Borovik, Anna
Auflage: 2010 edition
Hersteller: Springer US
Springer Nature Singapore
Maße: 237 x 156 x 15 mm
Von/Mit: Alexandre V Borovik (u. a.)
Erscheinungsdatum: 10.11.2009
Gewicht: 0,28 kg
preigu-id: 101558053
Zusammenfassung
"Mirrors and Reflections" is 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. The exposition is directed at advanced undergraduates and first-year graduate students, and features a large number of exercises at various levels of difficulty.
Inhaltsverzeichnis
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.
Details
Medium: Taschenbuch
Seiten: 172
Inhalt: xii
172 S.
74 s/w Illustr.
172 p. 74 illus.
ISBN-13: 9780387790657
ISBN-10: 0387790659
Sprache: Englisch
Herstellernummer: 11560760
Einband: Kartoniert / Broschiert
Autor: Borovik, Alexandre V
Borovik, Anna
Auflage: 2010 edition
Hersteller: Springer US
Springer Nature Singapore
Maße: 237 x 156 x 15 mm
Von/Mit: Alexandre V Borovik (u. a.)
Erscheinungsdatum: 10.11.2009
Gewicht: 0,28 kg
preigu-id: 101558053
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