Quadrangular algebras / Richard M. Weiss.

Format:

Book

Author/Creator:

Weiss, Richard M. (Richard Mark), 1946-

Series:

Mathematical notes (Princeton University Press) ; 46.

Princeton paperbacks.

Mathematical notes ; 46

Princeton paperbacks

Language:

English

Subjects (All):

Forms, Quadratic.

Algebra.

Physical Description:

1 online resource (146 p.)

Edition:

Course Book

Place of Publication:

Princeton, N.J. : Princeton University Press, c2006.

Language Note:

English

Summary:

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.

Contents:

Frontmatter

Contents

Preface

Chapter One. Basic Definitions

Chapter Two. Quadratic Forms

Chapter Three. Quadrangular Algebras

Chapter Four. Proper Quadrangular Algebras

Chapter Five. Special Quadrangular Algebras

Chapter Six. Regular Quadrangular Algebras

Chapter Seven. Defective Quadrangular Algebras

Chapter Eight. Isotopes

Chapter Nine. Improper Quadrangular Algebras

Chapter Ten. Existence

Chapter Eleven. Moufang Quadrangles

Chapter Twelve. The Structure Group

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. [133]) and index.

ISBN:

9786612129469

9781282129467

1282129465

9781400826940

1400826942

OCLC:

362799544