
Preview Material  Table of Contents  Index  Supplementary Material 
Mathematical Surveys and Monographs 2013; 276 pp; hardcover Volume: 191 ISBN10: 0821849379 ISBN13: 9780821849378 List Price: US$98 Member Price: US$78.40 Order Code: SURV/191 See also: Graduate Algebra: Noncommutative View  Louis Halle Rowen Lectures on Division Algebras  David J Saltman Multiantenna Channels: Capacity, Coding and Signal Processing  Gerard J Foschini and Sergio Verdu  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 SkolemNoether 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. Readership Graduate students and research mathematicians interested in central simple algebras, coding theory, and wireless communications. 


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