An Introduction to Central Simple Algebras and Their Applications to Wireless Communication
An Introduction to Central Simple Algebras and Their Applications to Wireless Communication
复制标题
中心简单代数简介及其在无线通信中的应用
DOI：
--
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
F. Oggier
中科院分区：
文献类型：
--
作者：
G. Berhuy;F. Oggier
中心简单代数自然地出现在数学的许多领域。它们与环理论密切相关，但在表示论、代数几何和数论中也很重要。最近，中心简单代数理论在无线通信编码中出现了令人惊讶的应用。书中的论述利用了这一意外发现，介绍了中心简单代数理论及其在编码理论中的应用。标准理论的许多结果或结构以经典形式呈现，但重点是明确的技术和示例，通常来自编码理论。主题包括四元数代数，分裂场，斯科勒姆-诺特定理，布劳尔群，交叉积，循环代数和酉对合代数。代码结构为许多示例和显式计算提供了机会。这本书提供了一个介绍中心代数的理论可访问的研究生，同时也提出了在无线通信的编码理论为数学观众的主题。它也适合于有兴趣学习除法代数如何在无线通信编码中有用的编码理论家。
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.
简单代数群和李代数中的单能类和幂零类
DOI：
--
发表时间：
2012
期刊：
--
影响因子：
--
作者：
Liebeck, Martin W.;Seitz, Gary M.
通讯作者：
Seitz, Gary M.