**Mathematical Surveys and Monographs**

Volume: 191;
2013;
276 pp;
Hardcover

MSC: Primary 12;
Secondary 11; 16

Print ISBN: 978-0-8218-4937-8

Product Code: SURV/191

List Price: $98.00

Individual Member Price: $78.40

**Electronic ISBN: 978-1-4704-0996-8
Product Code: SURV/191.E**

List Price: $98.00

Individual Member Price: $78.40

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#### Supplemental Materials

# An Introduction to Central Simple Algebras and Their Applications to Wireless Communication

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*Grégory Berhuy; Frédérique Oggier*

Central simple algebras arise naturally in
many areas of mathematics. They are closely connected with ring
theory, but are also important in representation theory, algebraic
geometry and number theory.

Recently, surprising applications of the theory of central simple
algebras have arisen in the context of coding for wireless
communication. The exposition in the book takes advantage of this
serendipity, presenting an introduction to the theory of central
simple algebras intertwined with its applications to coding theory.
Many results or constructions from the standard theory are presented
in classical form, but with a focus on explicit techniques and
examples, often from coding theory.

Topics covered include quaternion algebras, splitting fields, the
Skolem-Noether Theorem, the Brauer group, crossed products, cyclic
algebras and algebras with a unitary involution. Code constructions
give the opportunity for many examples and explicit computations.

This book provides an introduction to the theory of central
algebras accessible to graduate students, while also presenting topics
in coding theory for wireless communication for a mathematical
audience. It is also suitable for coding theorists interested in
learning how division algebras may be useful for coding in wireless
communication.

#### Table of Contents

# Table of Contents

## An Introduction to Central Simple Algebras and Their Applications to Wireless Communication

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Foreword vii8 free
- Introduction 110 free
- Central simple algebras 312 free
- Quaternion algebras 2130
- Fundamental results on central simple algebras 3140
- Splitting fields of central simple algebras 5362
- The Brauer group of a field 7988
- Crossed products 101110
- Cyclic algebras 129138
- Central simple algebras of degree 4 165174
- Central simple algebras with unitary involutions 189198
- Tensor products 231240
- A glimpse of number theory 249258
- Complex ideal lattices 265274
- Bibliography 271280
- Index 275284 free
- Back Cover Back Cover1287

#### Readership

Graduate students and research mathematicians interested in central simple algebras, coding theory, and wireless communications.