An Introduction to Nonassociative AlgebrasCourier Corporation, 13 déc. 2017 - 166 pages "An important addition to the mathematical literature … contains very interesting results not available in other books; written in a plain and clear style, it reads very smoothly." — Bulletin of the American Mathematical Society This concise study was the first book to bring together material on the theory of nonassociative algebras, which had previously been scattered throughout the literature. It emphasizes algebras that are, for the most part, finite-dimensional over a field. Written as an introduction for graduate students and other mathematicians meeting the subject for the first time, the treatment's prerequisites include an acquaintance with the fundamentals of abstract and linear algebra. After an introductory chapter, the book explores arbitrary nonassociative algebras and alternative algebras. Subsequent chapters concentrate on Jordan algebras and power-associative algebras. Throughout, an effort has been made to present the basic ideas, techniques, and flavor of what happens when the associative law is not assumed. Many of the proofs are given in complete detail. |
Table des matières
Preface | 1 |
Arbitrary Nonassociative Algebras | 9 |
Alternative Algebras | 27 |
Jordan Algebras | 91 |
Central Simple Jordan Algebras | 100 |
Derivations Simple Lie Algebras of Type F | 109 |
Simple Lie Algebras of Type Ee | 119 |
PowerAssociative Algebras | 128 |
Bibliography | 148 |
| 161 | |
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Expressions et termes fréquents
Albert algebra over F alternative algebra QI Amer arbitrary field associative algebra assume basis bimodule called Cayley algebra Chapter Clearly commutative contains contradiction Conversely Corollary defined dimension division algebra element equivalent exceptional exists extension F of characteristic field F finite finite-dimensional follows given Hence holds homomorphism ideal of QI identity implies induction inner involution isomorphic Jordan algebra L(QI Lemma Let QI linear operators mapping Math matrix maximal multiplication nilalgebra nilpotent nondegenerate Note obtain pairwise orthogonal Peirce decomposition power-associative algebra primitive proof properties Proposition prove QI over F Qſo quadratic R(QI radical relative ring satisfying scalar seen semisimple separable Similarly simple algebra simple Jordan algebra simple Lie algebras solvable subalgebra subalgebra of QI subspace Theorem trace trace form unique write y in QI