Lectures on Quadratic Jordan Algebras
Author: Nathan Jacobson
Publisher:
Published: 1969
Total Pages: 396
ISBN-13:
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The Arithmetics of Quadratic Jordan Algebras
Author: Michel L. Racine
Publisher: American Mathematical Soc.
Published: 1973
Total Pages: 134
ISBN-13: 0821818368
DOWNLOAD EBOOKThe first step in obtaining an arithmetic theory for finite dimensional quadratic Jordan algebras over the quotient field of a Dedekind ring is the determination of maximal orders. This is the main concern of this paper. Jordan analogues of some of the first theorems in classical associative arithmetic are obtained. For special quadratic Jordan algebras, the problem of determining maximal orders is reduced to arithmetic questions in quadratic forms and associative algebras with involution. The number of isomorphism classes of maximal orders is computed for most central simple quadratic Jordan algebras over a local field. In the process, previous results of Knebusch are obtained in a uniform fashion and are extended to the case of algebras over fields of characteristic 2 and 3.
A Taste of Jordan Algebras
Author: Kevin McCrimmon
Publisher: Springer Science & Business Media
Published: 2006-05-29
Total Pages: 584
ISBN-13: 0387217967
DOWNLOAD EBOOKThis book describes the history of Jordan algebras and describes in full mathematical detail the recent structure theory for Jordan algebras of arbitrary dimension due to Efim Zel'manov. Jordan algebras crop up in many surprising settings, and find application to a variety of mathematical areas. No knowledge is required beyond standard first-year graduate algebra courses.
Jordan Algebras and Algebraic Groups
Author: Tonny A. Springer
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 181
ISBN-13: 3642619703
DOWNLOAD EBOOKFrom the reviews: "This book presents an important and novel approach to Jordan algebras. [...] Springer's work will be of service to research workers familiar with linear algebraic groups who find they need to know something about Jordan algebras and will provide Jordan algebraists with new techniques and a new approach to finite-dimensional algebras over fields." American Scientist
The Scalar Center for Quadratic Jordan Algebras
Author: Bernard Ives Fulgham
Publisher:
Published: 2002
Total Pages: 120
ISBN-13:
DOWNLOAD EBOOKLinear Algebraic Groups
Author: T.A. Springer
Publisher: Springer Science & Business Media
Published: 2010-10-12
Total Pages: 347
ISBN-13: 0817648402
DOWNLOAD EBOOKThe first edition of this book presented the theory of linear algebraic groups over an algebraically closed field. The second edition, thoroughly revised and expanded, extends the theory over arbitrary fields, which are not necessarily algebraically closed. It thus represents a higher aim. As in the first edition, the book includes a self-contained treatment of the prerequisites from algebraic geometry and commutative algebra, as well as basic results on reductive groups. As a result, the first part of the book can well serve as a text for an introductory graduate course on linear algebraic groups.
Modules and Algebras
Author: Robert Wisbauer
Publisher: CRC Press
Published: 1996-05-15
Total Pages: 384
ISBN-13: 9780582289819
DOWNLOAD EBOOKModule theory over commutative asociative rings is usually extended to noncommutative associative rings by introducing the category of left (or right) modules. An alternative to this procedure is suggested by considering bimodules. A refined module theory for associative rings is used to investigate the bimodule structure of arbitary algebras and group actions on these algebras.
Jordan Algebras
Author: Wilhelm Kaup
Publisher: Walter de Gruyter
Published: 2011-05-02
Total Pages: 353
ISBN-13: 3110878119
DOWNLOAD EBOOKThe series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Descent in Buildings (AM-190)
Author: Bernhard Mühlherr
Publisher: Princeton University Press
Published: 2015-09-22
Total Pages: 353
ISBN-13: 1400874017
DOWNLOAD EBOOKDescent in Buildings begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. The authors then put their algebraic solution into a geometric context by developing a general fixed point theory for groups acting on buildings of arbitrary type, giving necessary and sufficient conditions for the residues fixed by a group to form a kind of subbuilding or "form" of the original building. At the center of this theory is the notion of a Tits index, a combinatorial version of the notion of an index in the relative theory of algebraic groups. These results are combined at the end to show that every exceptional Bruhat-Tits building arises as a form of a "residually pseudo-split" Bruhat-Tits building. The book concludes with a display of the Tits indices associated with each of these exceptional forms. This is the third and final volume of a trilogy that began with Richard Weiss' The Structure of Spherical Buildings and The Structure of Affine Buildings.
Finite-Dimensional Division Algebras over Fields
Author: Nathan Jacobson
Publisher: Springer Science & Business Media
Published: 2009-12-09
Total Pages: 290
ISBN-13: 3642024297
DOWNLOAD EBOOKHere, 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.
