Cyclic Division Algebras PDF Download
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Author | : Frdrique Oggier |
Publisher | : Now Publishers Inc |
Total Pages | : 109 |
Release | : 2007 |
Genre | : Computers |
ISBN | : 1601980507 |
Download Cyclic Division Algebras Book in PDF, ePub and Kindle
Multiple antennas at both the transmitter and receiver ends of a wireless digital transmission channel may increase both data rate and reliability. Reliable high rate transmission over such channels can only be achieved through Space-Time coding. Rank and determinant code design criteria have been proposed to enhance diversity and coding gain. The special case of full-diversity criterion, requires that the difference of any two distinct codewords has full rank. Extensive work has been done on Space-Time coding, aiming to attain fully diverse codes with high rate. Division algebras have been proposed as a new tool for constructing Space-Time codes, since they are non-commutative algebras that naturally yield linear fully diverse codes. Their algebraic properties can thus be further exploited to improve the design of good codes. Cyclic Division Algebras: A Tool for Space-Time Coding provides a tutorial introduction to the algebraic tools involved in the design of codes based on division algebras. The different design criteria involved are illustrated, including the constellation shaping, the information lossless property, the non-vanishing determinant property and the diversity multiplexing tradeoff. Finally complete mathematical background underlying the construction of the Golden code and the other Perfect Space-Time block codes is given. Cyclic Division Algebras: A Tool for Space-Time Coding is for students, researchers and professionals working on wireless communication systems.
Author | : Nathan Jacobson |
Publisher | : Springer Science & Business Media |
Total Pages | : 290 |
Release | : 2009-12-09 |
Genre | : Mathematics |
ISBN | : 3642024297 |
Download Finite-Dimensional Division Algebras over Fields Book in PDF, ePub and Kindle
Here, the eminent algebraist, Nathan Jacobsen, concentrates on those algebras that have an involution. Although they appear in many contexts, these algebras first arose in the study of the so-called "multiplication algebras of Riemann matrices". Of particular interest are the Jordan algebras determined by such algebras, and thus their structure is discussed in detail. Two important concepts also dealt with are the universal enveloping algebras and the reduced norm. However, the largest part of the book is the fifth chapter, which focuses on involutorial simple algebras of finite dimension over a field.
Author | : Abraham Adrian Albert |
Publisher | : American Mathematical Soc. |
Total Pages | : 224 |
Release | : 1939-12-31 |
Genre | : Mathematics |
ISBN | : 0821810243 |
Download Structure of Algebras Book in PDF, ePub and Kindle
The first three chapters of this work contain an exposition of the Wedderburn structure theorems. Chapter IV contains the theory of the commutator subalgebra of a simple subalgebra of a normal simple algebra, the study of automorphisms of a simple algebra, splitting fields, and the index reduction factor theory. The fifth chapter contains the foundation of the theory of crossed products and of their special case, cyclic algebras. The theory of exponents is derived there as well as the consequent factorization of normal division algebras into direct factors of prime-power degree. Chapter VI consists of the study of the abelian group of cyclic systems which is applied in Chapter VII to yield the theory of the structure of direct products of cyclic algebras and the consequent properties of norms in cyclic fields. This chapter is closed with the theory of $p$-algebras. In Chapter VIII an exposition is given of the theory of the representations of algebras. The treatment is somewhat novel in that while the recent expositions have used representation theorems to obtain a number of results on algebras, here the theorems on algebras are themselves used in the derivation of results on representations. The presentation has its inspiration in the author's work on the theory of Riemann matrices and is concluded by the introduction to the generalization (by H. Weyl and the author) of that theory. The theory of involutorial simple algebras is derived in Chapter X both for algebras over general fields and over the rational field. The results are also applied in the determination of the structure of the multiplication algebras of all generalized Riemann matrices, a result which is seen in Chapter XI to imply a complete solution of the principal problem on Riemann matrices.
Author | : M. Denert |
Publisher | : |
Total Pages | : 178 |
Release | : 198? |
Genre | : |
ISBN | : |
Download The Level of Cyclic Division Algebras Book in PDF, ePub and Kindle
Author | : Bharath Al Sethuraman |
Publisher | : |
Total Pages | : 170 |
Release | : 1991 |
Genre | : |
ISBN | : |
Download Constructions of Valued Division Algebras with Applications to Indecomposability and Elementary Abelian Crossed Products Book in PDF, ePub and Kindle
Author | : Jean Bernard Nganou |
Publisher | : |
Total Pages | : 140 |
Release | : 2009 |
Genre | : Algebra, Abstract |
ISBN | : |
Download Decomposition of Division Algebras Into Tensor Product of Cyclic Algebras Book in PDF, ePub and Kindle
Author | : John Dauns |
Publisher | : |
Total Pages | : 446 |
Release | : 1982 |
Genre | : Mathematics |
ISBN | : |
Download A Concrete Approach to Division Rings Book in PDF, ePub and Kindle
Author | : A. A. Albert |
Publisher | : American Mathematical Soc. |
Total Pages | : 224 |
Release | : 1964 |
Genre | : Algebraic fields |
ISBN | : 0821874608 |
Download Structure of Algebras Book in PDF, ePub and Kindle
Author | : Frank Hung-Yueh Chang |
Publisher | : |
Total Pages | : 276 |
Release | : 2004 |
Genre | : |
ISBN | : |
Download Division Algebras Over Generalized Local Fields Book in PDF, ePub and Kindle
Author | : Grégory Berhuy |
Publisher | : American Mathematical Soc. |
Total Pages | : 288 |
Release | : 2013-07-05 |
Genre | : Mathematics |
ISBN | : 0821849379 |
Download An Introduction to Central Simple Algebras and Their Applications to Wireless Communication Book in PDF, ePub and Kindle
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.