Jordan Algebras and Algebraic Groups
(Sprache: Englisch)
The aim of this book is to give an exposition of a part of the theory of Jordan algebras, using linear algebraic groups. That such groups play a role in Jordan algebra theory is a well-established fact, pointed out, for example, by H. Braun and M. Koecher...
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Produktinformationen zu „Jordan Algebras and Algebraic Groups “
Klappentext zu „Jordan Algebras and Algebraic Groups “
The aim of this book is to give an exposition of a part of the theory of Jordan algebras, using linear algebraic groups. That such groups play a role in Jordan algebra theory is a well-established fact, pointed out, for example, by H. Braun and M. Koecher in their book "Jordan Algebren". We have tried to exploit that fact as much as possible. In particular, the classification of simple Jordan algebras is derived here from the Cartan-Chevalley theory of semi-simple linear algebraic groups and their irreducible representations.
Inhaltsverzeichnis zu „Jordan Algebras and Algebraic Groups “
Preliminaries.- J-structures.- Examples.- The Quadratic Map of a J-structure.- The Lie Algebras Associates with a J-structure.- J-structures of Low Degree.- Relation with Jordan Algebras.- Relation with Quadratic Jordan Algebras.- The Minimum Polynomial of an Element.- Ideals, the Radical.- Peirce Decomposition Defined by an Idempotent Element.- Classification of Certain Algebraic Groups. Strongly Simple J-structures.- Simple J-structures.- The Structure Group of a Simple J-structure and the Related Lie Algebras.- Rationality Questions.
Autoren-Porträt von Tonny A. Springer
Biography of Tonny A. Springer
Born on February 13, 1926 at the Hague, Holland, Tonny A. Springer studied mathematics at the University of Leiden, obtaining his Ph. D. in 1951. He has been at the University of Utrecht since 1955, from 1959-1991 as a full professor, and since 1991 as an emeritus professor.
He has held visiting positions at numerous prestigious institutions all over the globe, including the Institute for Advanced Study (Princeton), the Institut des Hautes Etudes Scientifiques (Bures-sur-Yvette) and the Tata Institute of Fundamental Research (Bombay).
Throughout his career T. A. Springer has been involved in research on various aspects of the theory of linear algebraic groups (conjugacy classes, Galois cohomology, Weyl groups).
Bibliographische Angaben
- Autor: Tonny A. Springer
- 1998, 184 Seiten, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3540636323
- ISBN-13: 9783540636328
- Erscheinungsdatum: 11.12.1997
Sprache:
Englisch
Rezension zu „Jordan Algebras and Algebraic Groups “
From the reviews: "This book presents an important and novel approach to Jordan algebras. Jordan algebras have come to play a role in many areas of mathematics, including Lie algebras and the geometry of Chevalley groups. 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) "By placing the classification of Jordan algebras in the perspective of classification of certain root systems, the book demonstrates that the structure theories associative, Lie, and Jordan algebras are not separate creations but rather instances of the one all-encompassing miracle of root systems. ..." (Math. Reviews)
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