An introduction to central simple algebras and their applications to wireless communication

著者

• Berhuy, Grégory
• Oggier, Frédérique

書誌事項

An introduction to central simple algebras and their applications to wireless communication

Grégory Berhuy, Frédérique Oggier

（Mathematical surveys and monographs, v. 191）

American Mathematical Society, c2013

注記

Includes bibliographical references (p. 271-273) and index

内容説明・目次

内容説明

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.

目次

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

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詳細情報

• NII書誌ID(NCID): BB13033761
• ISBN:
  • 9780821849378
• LCCN: 2013009629
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: viii, 276 p.
• 大きさ: 26 cm
• 分類:
  • LCC : QA247.45
  • DC23 : 512/.3
• 件名:
  • LCSH : Division algebras
  • LCSH : Skew fields
• 親書誌ID:
  • BA00134419