An introduction to central simple algebras and their applications to wireless communication
Author(s)
Bibliographic Information
An introduction to central simple algebras and their applications to wireless communication
（Mathematical surveys and monographs, v. 191）
American Mathematical Society, c2013
Available at 37 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
S||MSM||191200026147580
Note
Includes bibliographical references (p. 271-273) and index
Description and Table of Contents
Description
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
Foreword
Introduction
Central simple algebras
Quaternion algebras
Fundamental results on central simple algebras
Splitting fields of central simple algebras
The Brauer group of a field
rossed products
Cyclic algebras
Central simple algebras of degree 4
Central simple algebras with unitary involutions
Tensor products
A glimpse of number theory
Complex ideal lattices
Bibliography
Index
by "Nielsen BookData"