Jordan Algebras and Algebraic Groups [Paperback]

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

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)? 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.From the reviews: This book presents an important and novel approach to Jordan algebras. Jordan algebras have come lóÑ