Quadrangular Algebras. (MN-46)

Nonfiction, Science & Nature, Mathematics, Algebra
Cover of the book Quadrangular Algebras. (MN-46) by Richard M. Weiss, Princeton University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Richard M. Weiss ISBN: 9781400826940
Publisher: Princeton University Press Publication: February 9, 2009
Imprint: Princeton University Press Language: English
Author: Richard M. Weiss
ISBN: 9781400826940
Publisher: Princeton University Press
Publication: February 9, 2009
Imprint: Princeton University Press
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Princeton University Press

Cover of the book The Oceans by Richard M. Weiss
Cover of the book Power over Peoples by Richard M. Weiss
Cover of the book Kant's Philosophical Revolution by Richard M. Weiss
Cover of the book Ever the Leader by Richard M. Weiss
Cover of the book Friendly Fire by Richard M. Weiss
Cover of the book The Original Folk and Fairy Tales of the Brothers Grimm by Richard M. Weiss
Cover of the book Topics in Commutative Ring Theory by Richard M. Weiss
Cover of the book The Life of Roman Republicanism by Richard M. Weiss
Cover of the book Banding Together by Richard M. Weiss
Cover of the book The Mexican Heartland by Richard M. Weiss
Cover of the book Putting Liberalism in Its Place by Richard M. Weiss
Cover of the book Political Bubbles by Richard M. Weiss
Cover of the book Prison Religion by Richard M. Weiss
Cover of the book The Theory of Island Biogeography Revisited by Richard M. Weiss
Cover of the book The Complete Works of Aristotle by Richard M. Weiss
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy