Quadrangular Algebras - Richard M. Weiss

Quadrangular Algebras

Buch | Softcover
144 Seiten
2005
Princeton University Press (Verlag)
978-0-691-12460-5 (ISBN)
87,25 inkl. MwSt
Based on their relationship to exceptional algebraic groups, quadrangular algebras belong in a series together with alternative and Jordan division algebras, this book introduces a class of non-associative algebras related to exceptional algebraic groups and their associated buildings.
This book introduces a new class of non-associative algebras related to certain exceptional algebraic groups and their associated buildings. Richard Weiss develops a theory of these "quadrangular algebras" that opens the first purely algebraic approach to the exceptional Moufang quadrangles. These quadrangles include both those that arise as the spherical buildings associated to groups of type E6, E7, and E8 as well as the exotic quadrangles "of type F4" discovered earlier by Weiss. Based on their relationship to exceptional algebraic groups, quadrangular algebras belong in a series together with alternative and Jordan division algebras. Formally, the notion of a quadrangular algebra is derived from the notion of a pseudo-quadratic space (introduced by Jacques Tits in the study of classical groups) over a quaternion division ring. This book contains the complete classification of quadrangular algebras starting from first principles. It also shows how this classification can be made to yield the classification of exceptional Moufang quadrangles as a consequence. The book closes with a chapter on isotopes and the structure group of a quadrangular algebra.
Quadrangular Algebras is intended for graduate students of mathematics as well as specialists in buildings, exceptional algebraic groups, and related algebraic structures including Jordan algebras and the algebraic theory of quadratic forms.

Richard M. Weiss is William Walker Professor of Mathematics at Tufts University. He is the author of "The Structure of Spherical Buildings" (Princeton) and the coauthor (with Jacques Tits) of "Moufang Polygons". He received a Humboldt Research Prize in 2004.

Preface vii Chapter 1. Basic Definitions 1 Chapter 2. Quadratic Forms 11 Chapter 3. Quadrangular Algebras 21 Chapter 4. Proper Quadrangular Algebras 29 Chapter 5. Special Quadrangular Algebras 37 Chapter 6. Regular Quadrangular Algebras 45 Chapter 7. Defective Quadrangular Algebras 59 Chapter 8. Isotopes 77 Ch apter 9. Improp er Quadrangu lar Algebras 83 Chapter 10. Existence 95 Chapter 11. Moufang Quadrangles 109 Chapter 12. The Structure Group 125 Bibliography 133 Index 134

Erscheint lt. Verlag 9.10.2005
Reihe/Serie Mathematical Notes
Zusatzinfo 1 line illus.
Verlagsort New Jersey
Sprache englisch
Maße 152 x 235 mm
Gewicht 198 g
Themenwelt Mathematik / Informatik Mathematik Arithmetik / Zahlentheorie
ISBN-10 0-691-12460-4 / 0691124604
ISBN-13 978-0-691-12460-5 / 9780691124605
Zustand Neuware
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