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100301s2010 xxu| s |||| 0|eng d |
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|a 9780387790664
|9 978-0-387-79066-4
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|a 10.1007/978-0-387-79066-4
|2 doi
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|a QA174-183
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|a PBG
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|a MAT002010
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|a 512.2
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|a Borovik, Alexandre V.
|e author.
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|a Mirrors and Reflections
|c by Alexandre V. Borovik, Anna Borovik.
|h [electronic resource] /
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|a New York, NY :
|b Springer New York,
|c 2010.
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| 300 |
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|b online resource.
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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|a text file
|b PDF
|2 rda
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|a Universitext
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|a 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 AnŁ1, 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.
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|a 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.
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| 650 |
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|a Mathematics.
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| 650 |
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|a Group theory.
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| 650 |
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|a Matrix theory.
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| 650 |
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|a Topological Groups.
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| 650 |
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|a Geometry.
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| 650 |
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|a Mathematical physics.
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| 650 |
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4 |
|a Mathematics.
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| 650 |
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|a Group Theory and Generalizations.
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| 650 |
2 |
4 |
|a Geometry.
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| 650 |
2 |
4 |
|a Topological Groups, Lie Groups.
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| 650 |
2 |
4 |
|a Linear and Multilinear Algebras, Matrix Theory.
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| 650 |
2 |
4 |
|a Mathematical Methods in Physics.
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| 700 |
1 |
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|a Borovik, Anna.
|e author.
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| 710 |
2 |
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|a SpringerLink (Online service)
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|t Springer eBooks
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| 776 |
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|i Printed edition:
|z 9780387790657
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| 830 |
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|a Universitext
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|u https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-387-79066-4
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| 912 |
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|a ZDB-2-SMA
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| 950 |
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|a Mathematics and Statistics (Springer-11649)
|