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Cyclic Division Algebras

2007 Computers
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Release : 2007
Genre : Computers
Kind : eBook
Book Rating : 507/5 ( reviews)

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Book Synopsis Cyclic Division Algebras by : Frdrique Oggier

Download or read book Cyclic Division Algebras written by Frdrique Oggier. This book was released on 2007. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Finite-Dimensional Division Algebras over Fields

2009-12-09 Mathematics
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Release : 2009-12-09
Genre : Mathematics
Kind : eBook
Book Rating : 297/5 ( reviews)

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Book Synopsis Finite-Dimensional Division Algebras over Fields by : Nathan Jacobson

Download or read book Finite-Dimensional Division Algebras over Fields written by Nathan Jacobson. This book was released on 2009-12-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Structure of Algebras

1939-12-31 Mathematics
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Release : 1939-12-31
Genre : Mathematics
Kind : eBook
Book Rating : 243/5 ( reviews)

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Book Synopsis Structure of Algebras by : Abraham Adrian Albert

Download or read book Structure of Algebras written by Abraham Adrian Albert. This book was released on 1939-12-31. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Level of Cyclic Division Algebras

198?
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Release : 198?
Genre :
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Book Synopsis The Level of Cyclic Division Algebras by : M. Denert

Download or read book The Level of Cyclic Division Algebras written by M. Denert. This book was released on 198?. Available in PDF, EPUB and Kindle. Book excerpt:

Constructions of Valued Division Algebras with Applications to Indecomposability and Elementary Abelian Crossed Products

1991
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Release : 1991
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Book Synopsis Constructions of Valued Division Algebras with Applications to Indecomposability and Elementary Abelian Crossed Products by : Bharath Al Sethuraman

Download or read book Constructions of Valued Division Algebras with Applications to Indecomposability and Elementary Abelian Crossed Products written by Bharath Al Sethuraman. This book was released on 1991. Available in PDF, EPUB and Kindle. Book excerpt:

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