The Arithmetics Of Quadratic Jordan Algebras

Author : Michel L. Racine
Publisher : American Mathematical Soc.
Page : 134 pages
File Size : 45,5 Mb
Release : 1973
Category : Algèbres associatives
ISBN : 9780821818367

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The Arithmetics of Quadratic Jordan Algebras by Michel L. Racine Pdf

The 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.

Author : Kevin McCrimmon
Publisher : Springer Science & Business Media
Page : 563 pages
File Size : 42,6 Mb
Release : 2006-05-29
Category : Mathematics
ISBN : 9780387217963

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A Taste of Jordan Algebras by Kevin McCrimmon Pdf

This 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.

Author : Michel L. Racine
Publisher : Unknown
Page : 128 pages
File Size : 43,5 Mb
Release : 1973
Category : Electronic
ISBN : OCLC:36946382

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Arithmetics of Quadratic Jordan Algebras by Michel L. Racine Pdf

Author : Tonny A. Springer
Publisher : Springer Science & Business Media
Page : 181 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642619700

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Jordan Algebras and Algebraic Groups by Tonny A. Springer Pdf

From 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

Author : Nathan Jacobson
Publisher : American Mathematical Soc.
Page : 464 pages
File Size : 53,6 Mb
Release : 1968-12-31
Category : Mathematics
ISBN : 9780821846407

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Structure and Representations of Jordan Algebras by Nathan Jacobson Pdf

The theory of Jordan algebras has played important roles behind the scenes of several areas of mathematics. Jacobson's book has long been the definitive treatment of the subject. It covers foundational material, structure theory, and representation theory for Jordan algebras. Of course, there are immediate connections with Lie algebras, which Jacobson details in Chapter 8. Of particular continuing interest is the discussion of exceptional Jordan algebras, which serve to explain the exceptional Lie algebras and Lie groups. Jordan algebras originally arose in the attempts by Jordan, von Neumann, and Wigner to formulate the foundations of quantum mechanics. They are still useful and important in modern mathematical physics, as well as in Lie theory, geometry, and certain areas of analysis.

Author : Nathan Jacobson
Publisher : Unknown
Page : 396 pages
File Size : 48,7 Mb
Release : 1969
Category : Jordan algebras
ISBN : UOM:39015035215584

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Lectures on Quadratic Jordan Algebras by Nathan Jacobson Pdf

Author : Max Koecher
Publisher : Springer
Page : 180 pages
File Size : 46,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540484028

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The Minnesota Notes on Jordan Algebras and Their Applications by Max Koecher Pdf

This volume contains a re-edition of Max Koecher's famous Minnesota Notes. The main objects are homogeneous, but not necessarily convex, cones. They are described in terms of Jordan algebras. The central point is a correspondence between semisimple real Jordan algebras and so-called omega-domains. This leads to a construction of half-spaces which give an essential part of all bounded symmetric domains. The theory is presented in a concise manner, with only elementary prerequisites. The editors have added notes on each chapter containing an account of the relevant developments of the theory since these notes were first written.

Author : John R. Faulkner
Publisher : American Mathematical Soc.
Page : 71 pages
File Size : 44,7 Mb
Release : 1970
Category : Mathematics
ISBN : 9780821818046

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Octonion Planes Defined by Quadratic Jordan Algebras by John R. Faulkner Pdf

Author : Nathan Jacobson
Publisher : Unknown
Page : 340 pages
File Size : 41,6 Mb
Release : 1981
Category : Jordan algebras
ISBN : UOM:39015015622411

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Structure Theory of Jordan Algebras by Nathan Jacobson Pdf

Author : Tonny Albert Springer
Publisher : Unknown
Page : 168 pages
File Size : 47,9 Mb
Release : 1998
Category : Electronic
ISBN : 0387636323

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Jordan Algebras and Algebraic Groups by Tonny Albert Springer Pdf

Author : Tonny A. Springer,Ferdinand D. Veldkamp
Publisher : Springer
Page : 212 pages
File Size : 49,9 Mb
Release : 2013-12-21
Category : Mathematics
ISBN : 9783662126226

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Octonions, Jordan Algebras and Exceptional Groups by Tonny A. Springer,Ferdinand D. Veldkamp Pdf

The 1963 Göttingen notes of T. A. Springer are well known in the field but have been unavailable for some time. This book is a translation of those notes, completely updated and revised. The part of the book dealing with the algebraic structures is on a fairly elementary level, presupposing basic results from algebra.

Author : Bernard Ives Fulgham
Publisher : Unknown
Page : 120 pages
File Size : 41,9 Mb
Release : 2002
Category : Electronic
ISBN : UVA:X004651619

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The Scalar Center for Quadratic Jordan Algebras by Bernard Ives Fulgham Pdf

Author : Erhard Neher
Publisher : Springer
Page : 206 pages
File Size : 43,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540479215

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Jordan Triple Systems by the Grid Approach by Erhard Neher Pdf

Grids are special families of tripotents in Jordan triple systems. This research monograph presents a theory of grids including their classification and coordinization of their cover. Among the applications given are - classification of simple Jordan triple systems covered by a grid, reproving and extending most of the known classification theorems for Jordan algebras and Jordan pairs - a Jordan-theoretic interpretation of the geometry of the 27 lines on a cubic surface - structure theories for Hilbert-triples and JBW*-triples, the Jordan analogues of Hilbert-triples and W*-algebras which describe certain symmetric Banach manifolds. The notes are essentially self-contained and independent of the structure theory of Jordan algebras and Jordan pairs. They can be read by anyone with a basic knowledge in algebraic geometry or functional analysis. The book is intended to serve both as a reference for researchers in Jordan theory and as an introductory textbook for newcomers to the subject.

Author : James D. Malley
Publisher : Springer Science & Business Media
Page : 110 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461226789

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Statistical Applications of Jordan Algebras by James D. Malley Pdf

This monograph brings together my work in mathematical statistics as I have viewed it through the lens of Jordan algebras. Three technical domains are to be seen: applications to random quadratic forms (sums of squares), the investigation of algebraic simplifications of maxi mum likelihood estimation of patterned covariance matrices, and a more wide open mathematical exploration of the algebraic arena from which I have drawn the results used in the statistical problems just mentioned. Chapters 1, 2, and 4 present the statistical outcomes I have developed using the algebraic results that appear, for the most part, in Chapter 3. As a less daunting, yet quite efficient, point of entry into this material, one avoiding most of the abstract algebraic issues, the reader may use the first half of Chapter 4. Here I present a streamlined, but still fully rigorous, definition of a Jordan algebra (as it is used in that chapter) and its essential properties. These facts are then immediately applied to simplifying the M:-step of the EM algorithm for multivariate normal covariance matrix estimation, in the presence of linear constraints, and data missing completely at random. The results presented essentially resolve a practical statistical quest begun by Rubin and Szatrowski [1982], and continued, sometimes implicitly, by many others. After this, one could then return to Chapters 1 and 2 to see how I have attempted to generalize the work of Cochran, Rao, Mitra, and others, on important and useful properties of sums of squares.

Author : Ricardo Baeza
Publisher : American Mathematical Soc.
Page : 424 pages
File Size : 54,9 Mb
Release : 2009-08-14
Category : Mathematics
ISBN : 9780821846483

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Quadratic Forms -- Algebra, Arithmetic, and Geometry by Ricardo Baeza Pdf

This volume presents a collection of articles that are based on talks delivered at the International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms held in Frutillar, Chile in December 2007. The theory of quadratic forms is closely connected with a broad spectrum of areas in algebra and number theory. The articles in this volume deal mainly with questions from the algebraic, geometric, arithmetic, and analytic theory of quadratic forms, and related questions in algebraic group theory and algebraic geometry.