Jordan algebras and algebraic groups

✍ Scribed by Springer, Tonny Albert

Publisher: Springer-Verlag
Year: 1973
Tongue: English
Leaves: 179
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete Bd. 75
Category: Library

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✦ Synopsis

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

✦ Table of Contents

Content: 0. Preliminaries.- 1. J-structures.- 2. Examples.- 3. The Quadratic Map of a J-structure.- 4. The Lie Algebras Associated with a J-structure.- 5. J-structures of Low Degree.- 6. Relation with Jordan Algebras (Characteristic ? 2).- 7. Relation with Quadratic Jordan Algebras.- 8. The Minimum Polynomial of an Element.- 9. Ideals, the Radical.- 10. Peirce Decomposition Defined by an Idempotent Element.- 11. Classification of Certain Algebraic Groups.- 12. Strongly Simple J-structures.- 13. Simple J-structures.- 14. The Structure Group of a Simple J-structure and the Related Lie Algebras.- 15. Rationality Questions.

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