# Mirrors and Reflections

• Alexandre V. Borovik
• Anna Borovik
Book

Part of the Universitext book series (UTX)

1. Front Matter
Pages i-xii
2. ### Geometric Background

1. Pages 11-16
2. Pages 17-23
3. Pages 25-34
3. ### Mirrors, Reflections, Roots

1. Pages 37-40
2. Pages 41-47
3. Pages 49-53
4. Pages 55-62
5. Pages 63-75
4. ### Coxeter Complexes

1. Pages 79-82
2. Pages 83-90
3. Pages 91-97
4. Pages 99-104
5. Pages 105-109
5. ### Classification

1. Pages 113-116
2. Pages 117-122
3. Pages 123-131
4. Pages 133-135
6. ### Three-Dimensional Reflection Groups

1. Pages 139-146

### Introduction

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.

### Keywords

Area Graph Group theory Permutation Sim Symmetry group algebra classification linear algebra

#### Authors and affiliations

• Alexandre V. Borovik
• 1
• Anna Borovik
1. 1.School of MathematicsUniversity of ManchesterManchesterUnited Kingdom

### Bibliographic information

• DOI https://doi.org/10.1007/978-0-387-79066-4
• Copyright Information Springer-Verlag New York 2010
• Publisher Name Springer, New York, NY
• eBook Packages Mathematics and Statistics
• Print ISBN 978-0-387-79065-7
• Online ISBN 978-0-387-79066-4