The Arithmetics Of Quadratic Jordan Algebras
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The Arithmetics Of Quadratic Jordan Algebras
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Author : Michel L. Racine
language : en
Publisher: American Mathematical Soc.
Release Date : 1973
The Arithmetics Of Quadratic Jordan Algebras written by Michel L. Racine and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Algèbres associatives categories.
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.
Arithmetics Of Quadratic Jordan Algebras
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Author : Michel L. Racine
language : en
Publisher:
Release Date : 1973
Arithmetics Of Quadratic Jordan Algebras written by Michel L. Racine and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with categories.
A Taste Of Jordan Algebras
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Author : Kevin McCrimmon
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-29
A Taste Of Jordan Algebras written by Kevin McCrimmon and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-29 with Mathematics categories.
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.
Lectures On Quadratic Jordan Algebras
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Author : Nathan Jacobson
language : en
Publisher:
Release Date : 1969
Lectures On Quadratic Jordan Algebras written by Nathan Jacobson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Jordan algebras categories.
Jordan Algebras And Algebraic Groups
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Author : Tonny A. Springer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Jordan Algebras And Algebraic Groups written by Tonny A. Springer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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
Structure And Representations Of Jordan Algebras
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Author : Nathan Jacobson
language : en
Publisher: American Mathematical Soc.
Release Date : 1968-12-31
Structure And Representations Of Jordan Algebras written by Nathan Jacobson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968-12-31 with Mathematics categories.
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.
Octonion Planes Defined By Quadratic Jordan Algebras
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Author : John R. Faulkner
language : en
Publisher: American Mathematical Soc.
Release Date : 1970
Octonion Planes Defined By Quadratic Jordan Algebras written by John R. Faulkner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.
The Minnesota Notes On Jordan Algebras And Their Applications
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Author : Max Koecher
language : en
Publisher: Springer
Release Date : 2006-11-14
The Minnesota Notes On Jordan Algebras And Their Applications written by Max Koecher and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
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.
Jordan Algebras And Algebraic Groups
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Author : Tonny Albert Springer
language : en
Publisher:
Release Date : 1998
Jordan Algebras And Algebraic Groups written by Tonny Albert Springer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Structure Theory Of Jordan Algebras
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Author : Nathan Jacobson
language : en
Publisher:
Release Date : 1981
Structure Theory Of Jordan Algebras written by Nathan Jacobson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Jordan algebras categories.