Cyclic Division Algebras
Download Cyclic Division Algebras full books in PDF, epub, and Kindle. Read online free Cyclic Division Algebras ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Author | : Frdrique Oggier |
Publisher | : Now Publishers Inc |
Total Pages | : 109 |
Release | : 2007 |
Genre | : Computers |
ISBN | : 1601980507 |
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 |
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 |
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 | : |
Author | : Bharath Al Sethuraman |
Publisher | : |
Total Pages | : 170 |
Release | : 1991 |
Genre | : |
ISBN | : |
Author | : Jean Bernard Nganou |
Publisher | : |
Total Pages | : 140 |
Release | : 2009 |
Genre | : Algebra, Abstract |
ISBN | : |
Author | : John Dauns |
Publisher | : |
Total Pages | : 446 |
Release | : 1982 |
Genre | : Mathematics |
ISBN | : |
Author | : A. A. Albert |
Publisher | : American Mathematical Soc. |
Total Pages | : 224 |
Release | : 1964 |
Genre | : Algebraic fields |
ISBN | : 0821874608 |
Author | : Frank Hung-Yueh Chang |
Publisher | : |
Total Pages | : 276 |
Release | : 2004 |
Genre | : |
ISBN | : |
Author | : David J. Saltman |
Publisher | : American Mathematical Soc. |
Total Pages | : 130 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 0821809792 |
This volume is based on lectures on division algebras given at a conference held at Colorado State University. Although division algebras are a very classical object, this book presents this ""classical"" material in a new way, highlighting current approaches and new theorems, and illuminating the connections with a variety of areas in mathematics.