Lectures on Quadratic Jordan Algebras
Author: Nathan Jacobson
Publisher:
Published: 1969
Total Pages: 396
ISBN-13:
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Author: Nathan Jacobson
Publisher:
Published: 1969
Total Pages: 396
ISBN-13:
DOWNLOAD EBOOKAuthor: Nathan Jacobson
Publisher:
Published: 1969
Total Pages:
ISBN-13:
DOWNLOAD EBOOKAuthor: Max Koecher
Publisher: Springer
Published: 2006-11-14
Total Pages: 180
ISBN-13: 3540484027
DOWNLOAD EBOOKThis 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: 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.
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.
Author: Michel L. Racine
Publisher:
Published: 1973
Total Pages:
ISBN-13:
DOWNLOAD EBOOKAuthor: Nathan Jacobson
Publisher:
Published: 1981
Total Pages: 340
ISBN-13:
DOWNLOAD EBOOKAuthor: Nathan Jacobson
Publisher: American Mathematical Soc.
Published: 1968-12-31
Total Pages: 464
ISBN-13: 082184640X
DOWNLOAD EBOOKThe 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:
Publisher:
Published: 1969
Total Pages: 390
ISBN-13:
DOWNLOAD EBOOKAuthor: Nathan Jacobson
Publisher:
Published: 1964*
Total Pages: 592
ISBN-13:
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